I have to disagree with a lot of points on your post.
But there are already countless pokémon who do this very well, maybe better than 26 will ever do, so I ask you: What does 26 have to offer that stands out above all others?
Well, we have a stunning choice of 3 viable hazard removers in the current metagame (remember, we build for the current metagame) - namely Tornadus-T, Rotom-W, and Tapu Fini. Kitsunoh and Excadrill run their respective hazard control options, but they are almost always consistent enough to rely solely on them. Thus, "countless" is a bit of an overstatement - I count 3 (or generously 5).
CAP26 has a great matchup against some key Stealth Rock setters in the metagame - namely Mega Diancie, Garchomp, Landorus-T, Mega Crucibelle, and Mega Tyranitar. Even more niche Stealth Rock setters like Fidgit and Clefable have horrendous matchups against CAP26. Furthermore, it's hard for Heatran, the last common Stealth Rock setter I haven't listed, to come in safely against CAP26 due to the looming threat of Earth Power, so it's hard for Heatran to keep up Stealth Rock also, especially if CAP26 is healthy. Our resident Spikes setters - Ferrothorn, Arghonaut, and Greninja - admittedly have better matchups against CAP26, but CAP26 is free to switch into these Spikes with Levitate, Earth Power smacks up Greninja, and a lot of sets have Toxic to cripple Arghonaut.
On the other hand, the current Defoggers stand toe-to-toe with the Stealth Rock setters in the metagame. SR setters have, naturally, evolved to ward of Tornadus-T, which has been the most consistent hazard remover since USUM - we have 3 Rock-type Mega Pokemon (resist Hurricane and don't care about Knock Off), Garchomp (which runs Stone Edge), and Heatran (which resists Hurricane and usually carries a Z-Crystal). Rotom-W and Tapu Fini, on the other hand, are rather easy to chip down, meaning that they must be played well to stand up to these hazard setters. This isn't to say that these hazard removers are not effective - they are the premier hazard removers in the metagame, but CAP26 has some clear advantages over them.
Finally, the maximum amount of chip damage that Levitate CAP26 can take from hazards is 3% damage from Stealth Rock. Compared to Tornadus-T, which takes 25%, Rotom-W, which takes 12%, and Tapu Fini, who is vulnerable to all hazards.
So, what does CAP26 have that stands out above all the other 3 hazard setters in the metagame? Excellent matchups against metagame Stealth Rock setters, passable matchups against a couple of the Spikes setters, and resistance/immunity to most hazards. CAP26 can definitely act as a great hazard remover.
Now, if you have read up to this point but you haven't done or changed your mind about the Stealth Rock's effectiveness over hazard removal, I have one more thing to tell you: What does hazard removal do for CAP 26 at all?
What hazard removal does for CAP26 is threefold:
1) It ensures CAP26 has utility that it will use multiple times throughout the match that doesn't compete with Doom Desire.
2) It throws off the opposing team's tempo by pressuring opposing Stealth Rock setters from putting the hazards back up for a few crucial turns later with Doom Desire and Earth Power
3) It means CAP26's teammates can get in more easily.
What hazard removal does for CAP26 is solidify the idea of a pivot. Rapid Spin ensures that CAP26 will be pivoting in and out over the course of a match. Hazard removal is used more times than setting Stealth Rock, due to the omnipresence of Spikes in the current metagame, and even so, Rapid Spin is a reactive utility move, which, as we have established in this thread, is a better sort of utility move to use than a proactive utility move such as Stealth Rock.
Furthermore, CAP26 can place pressure on the opposing team with Doom Desire, use that pressure to get a Rapid Spin off, and, in particulary, continue to use that pressure to keep Stealth Rock off - Mega Diancie, Garchomp, Landorus-T, Mega Crucibelle, and Mega Tyranitar don't want to switch into Doom Desire and don't really want to switch in the turn before Doom Desire either due to it hitting the next turn. Furthermore, Heatran is terrified of being eviscerated by Earth Power.
Now, we've championed Doom Desire as a move that you "checkmate" the opponent into by switching to a teammate. Well, I think it makes sense that Pokemon that has a
phenomonal set of traits by typing and ability to remove hazards should be able to exert that sort of hazard control, so that its teammates can get in more easily. CAP26 can get rid of the Spikes that wear down Mega Mawile and Mega Medicham, the Stealth Rock that plagues Choice Scarf Volkraken and Aurumoth, and the Toxic Spikes that cripple Arghonaut and Tangrowth.
Unlike Spikes, Stealth Rock requires a single turn to be effectively used and encourages the use of DD and phazing to force pokémon out, further pressuring the opposing team. You can wondering: But can 26 really handle all of this? And I tell you: Yes, it can, a great typing, great stats, two amazing abilities and the right spread are more than enough for 26 play this role with mastery, just like an ancient killing machine awakening after centuries just to spread the suffer, the death and the chaos among your enemies.
Unlike Rapid Spin, which CAP26 should run on itself because then it can immediately switch to a teammate before those pesky hazards go back up again, hazards don't need to be set by CAP26 itself to lay down the pressure with Doom Desire and phazing. That can be done with other hazard setters in the metagame - you can let the hazards stay for a couple turns and position CAP26 into a position to start phazing. But CAP26 to set Stealth Rock itself to use shuffling effectively? That's not necessary.
Furthermore, CAP26 doesn't have good matchups with opposing hazard removers. CAP26 does pressure Tornadus-T with Doom Desire, but Tornadus-T can use Knock Off and get rid of CAP26's precious Leftovers - which it really needs since 50% recovery and Leech Seed are now banned. Tapu Fini now runs Scald, which can inflict a burn (negates Leftovers) against Levitate CAP26, and while it's just a 3HKO, CAP26 doesn't have an especially good matchup against it. CAP26 is barely able to eat 2 Rotom-W Hydro Pumps with the Jordy's sample EV spread. With no good recovery, that's a losing matchup, especially considering CAP26's best retaliation is Toxic. This means CAP26 would face a similar problem Snaelstrom has with setting up hazards - it just can't keep them up well against the good hazard removers, which means that I don't think CAP26 can really play the Stealth Rock-setting role all that well.
So it came to my mind the Doom Desire + phazing set, which can be incredibly successful (ask Slowking). On the other hand, I did not want to turn 26 into a Slowking's copy and wanted to give it a way phazing more effectively, so the idea of putting entry hazard on the set came up, as it fits in perfectly with phazing (checks Arghonaut).
Honestly, I wouldn't worry about turning into a copy of Slowking. We're learning about delayed damaging moves for a very different metagame (an OU-based metagame vs. NU) - taking a different approach than most people assumed we would (i.e. Regenerator + extensive coverage would be required to use the delayed moves effectively). At the very least, I don't think Stealth Rock really changes how similar we are to Slowking at this point - I think we've distinguished CAP26 from Slowking at this point.
