Ok, before I counter your arguments, I would like you to know that I was once adamantly supportive of a Manaphy rise but convinced otherwise so I understand your arguments, and I hope I'm not too harsh.
I'm going to make 2 posts in 1 day which is really unusual for me, usually it is 1 post a month lol.
Oh how deep this topic is. Manaphy's movepool is huge, having a wide selection of coverage. First off is water STAB. STAB is always important on a Pokemon, and Manaphy generally has two options to go when it comes to it. Scald and Surf, Scald usually being used for its 100% 30% burn chance, while still having a good base power at 80. Surf can also be used for securing more crucial KO's, none that I can think of off the top of my head, but the extra power is nice. Secondly, we have set up. Not that this is relevant, but it could be interesting to note that all of the S rank Pokemon have some sort of set up and there are sets that use them. Manaphy has access to Tail Glow and Calm Mind. Tail Glow is an amazing set up move, giving the user +3 in special attack every time used which is ridiculous. One of Manaphy's moves coming off a +3 special attack is going to hurt. Calm Mind can also be used on perhaps bulkier Manaphy sets, giving it a better chance to set up. And after a boost or two, an attack is still going to leave a dent. Not as much as a Tail Glow boosted, but you also receive a bit more bulk. In most cases, the first two move slots are staples on Manaphy, but don't have to be. But in this case, I am referring to the last two slots as "fillers". These can consist of Rain Dance, Ice Beam, Energy Ball, Hidden Power Fire, Psychic, Rest, Shadow Ball, Skill Swap, and Heart Swap. Since talking about all of these will make this extremely long, I will hide them.
As far as this goes, yes Manaphy has a (sort of) expansive movepool. What you need to factor in, is what it can fit onto one set. Manaphy's best set it TG + 3 attacks. Out of your three coverage options, you have your obligatory Water STAB, usually Ice Beam, and HP Fire. See any problems? Yes, you can't hit Mega Venusaur because it can tank a +6 Ice Beam from full.
Calcs:
+3 252 SpA Manaphy Ice Beam vs. 252 HP / 4 SpD Thick Fat Mega Venusaur: 174-206 (47.8 - 56.5%) -- 85.9% chance to 2HKO
252+ SpA Mega Venusaur Giga Drain vs. 80 HP / 0 SpD Manaphy: 258-306 (71.4 - 84.7%) -- guaranteed 2HKO after Leftovers recovery
+6 252 SpA Manaphy Ice Beam vs. 252 HP / 0 SpD Thick Fat Mega Venusaur: 280-330 (76.9 - 90.6%) -- guaranteed 2HKO
Manaphy doesn't even net a guaranteed 2HKO on Mega Venusaur, so it can switch in on the TG and gain enough health back on the Giga Drain in order to live another. It can even live a +6 Ice Beam and cripple Manaphy, leaving it to be picked off by another teammate. So, suppose you give up Ice Beam to run Psychic. Then you have nothing to hit the latis. If you give up HP Fire, then Ferrothorn walls you and can cripple you.
+3 252 SpA Manaphy Ice Beam vs. 252 HP / 168 SpD Ferrothorn: 156-184 (44.3 - 52.2%) -- guaranteed 3HKO after Leftovers recovery
+3 252 SpA Manaphy Surf vs. 72 HP / 0 SpD Latias: 122-144 (38.2 - 45.1%) -- guaranteed 3HKO
So in this case, at least something walls Manaphy on Balance/Stall. This isn't even counting Chansey, which can cripple you with Thunder Wave/Toxic as it lives even a +6 Surf. As far as the RD sets, or the CM sets, all they do is sacrifice Coverage for Bulk, meaning Manaphy can break even less things. They literally just remove moveslots of coverage from Manaphy while it already is almost short of it. Tail Glow is the only set Manaphy really needs.
Manaphy has decent defenses believe it or not. 100/100/100 is nothing to laugh at. Along with a pretty good defensive typing in Water, Manaphy will be sponging (hah no pun intended) hits allowing it to set up easier. The well known Tail Glow + Rain Dance set runs a bit of bulk allowing Manaphy eat up more hits than it normally would. This can be crucial in some cases, and not all Pokemon have the option to do this. The Calm Mind set is very usable, and effective. It runs 240 HP/252 Defense making Manaphy as bulky as possible while it sets up Calm Minds. With almost infinite recovery and status healing, Manaphy is the perfect stall breaker. Some other precautions can be ran for situations, but these will most likely be covered in the "items" section. I will leave you with some calcs that can be helpful. (I will only be using the CM set for the sake of me needing food)
The main thing about Manaphy's Bulk, is that it goes away while Manaphy sets up. Manaphy can't force switches because its attacks without boosting are piss-weak. Nothing fears an unboosted Scald, and will continue to hurt Manaphy as it sets up. Once Manaphy's bulk is compromised, it is super easily to revenge kill with faster threats. This is the main reason why Manaphy's "amazing" 100/100/100 bulk means nothing. Also, all of the calcs you posted are of Manaphy's absolute bulkiest and least viable set.
Team support? Nah. If you think about it, the more you go up on the viability, the less and less team support each Pokemon needs. When you get to S rank, it is usually at the lowest. Manaphy however, needs very little team support if any. It is match up based, but so is all of Pokemon. If your opponent is running Ferrothorn for their Manaphy check and you have HP Fire, Manaphy is 6-0ing the team by itself. You rarely see a Pokemon that can 6-0 teams by itself that are prepared for it. But honestly, TG + RD runs through stall by itself, with the only real answer being Unaware Clef, which still has trouble with Scald burns/Surf always being possible. If you look at the checks compendium, you will see Kyurem-B, Raikou, and Gyarados being listed as GSI (Guaranteed Switch Ins) though not a single one of them are able to switch in to a neutral +3 coverage move. So what I am trying to say in this part of my argument is basically Manaphy requires less team support than other S rank Pokemon in some cases and it can just win depending on match up.
As you said, Manaphy's team support depends on the matchup. It is a well known fact, that Manaphy is deadweight against offensive teams, because it is outspeed and 2HKO'ed by a ton of major offensive threats, and it needs a turn to set up. Against balance and stall, Manaphy is still very effective and requires little team support. I already proved above how it is unable to break every single stall mon because of its limited coverage and moveslots. What it really needs is a set-up opportunity. Stall carries phasers such as Quagsire (haze) and Skarmory (Whirlwind) which can stop Manaphy's sweep. TrickScarf Gothitelle is also a problem as it can trick Manaphy a scarf while it is boosting. Manaphy requires team support to remove these threats, as well as team support to remove faster threats on balance/bulky offense, because it is super easy to stop from sweeping.
This is the last part of my long argument, and is basically where I talk about the sets a bit more and put in anything else I forgot to talk about. So not only is Manaphy's movepool large, but so are the options of items it can run. Lefties is probably the most common for all of the sets, giving it passive recovery to prolong its stay on the field, which is something megas do not have access to I might add. Another very viable item is a Wacan Berry. So let me put you in a scenario. You have a TG up, just took out one of your opponent's Pokemon and there last check to Manaphy is an electric type such as Manectric, Raikou, Thundurus, Magnezone, etc. Wacan Berry allows you to take one of there electric STABS and kill it in return, leading to a win. So an item allows Manaphy to take off most Pokemon of one type off of the checks list, if played right. This is a huge difference. There are three more items Manaphy can run effectively to my knowledge. The next one is a Lum Berry. This is ran on non Rain Dance sets, and lets Manaphy bait the opponent in to going for a Twave or Spore or something to cripple Manaphy. You can then fire back a move to kill the mon or if you outspeed set up a TG then kill them. Life Orb is an option, but not very used. It adds power to Manaphy's hits, but severely limits the length of Manaphy in a battle. The final option is a Salac Berry. Salac Berry allows Manaphy to outspeed a lot of its checks after getting low in health. But does make it subject to priority. One thing I would like to add cause I forgot to put it anywhere else. Manaphy has a pretty great speed tier when considering the bulk that it has, it can outspeed a lot of things in the OU tier though not having the "magic" 110 speed.
Well, items don't actually add much to Manaphy's viability except for the Wacan berry, although a +3 Surf may not kill an offensive electric type, and the fact that electric attacks generally still do 50-60% through the Wacan Berry, which is no good if Manaphy is weakened as it would be over the course of a battle. Manaphy's speed is actually what makes it unviable. It is unable to outpeed key threats which allows it to be easily revenge killed its sweep to be stopped.
Some stuff I'll add:
Manaphy is a great mon, there is no doubt about that. It just doesn't dominate the metagame with its lacking stats, specifically its below par speed for its role, and its requirement to waste turns boosting. The combination of its low speed and its requirement to boost before actually being able to do anything are a real detriment to its viability.