While I would agree that Zapdos should go to S thanks to it's fantastic typing and BST distribution which lets it wall a helluva lot of stuff while maintaining good offensive presence, I'm slightly opposed to the fact that if it does get bumped up, Flying would then have 6 mons considered S Rank in viability. Going from nani's post that is quoted in the OP:
I'm not sure that having 6 mons, a whole team, classified in this way is what we're aiming to get from these rankings. It seems to me that splitting ranks could be useful here, and maybe moving 2 down to A+ would give a better indicative of what is classed as essential / extremely important.
On Slowbro, I would again agree that this should go to S. It literally fills a niche on Psychic that pretty much nothing else can, or at least it outclasses them. Your options for Physical wall on Psychic go: Mew, Slowbro, Cresselia, Jirachi and Deo-D. Out of these, Mew is better suited to Special walling and support roles, Cresselia is absolute set up bait to anything with taunt or substitute, Jirachi prefers special walling or offensive sets, and any role deo-d could use is generally outclassed by Mew, leaving Slowbro as the only true candidate. It's for this reason that it's so common on Psychic teams, as well as it's excellent movepool and stats, meaning it can be tailored to wall or remove certain threats. Overall a very deserving S Rank.
I'm fine with Pinsir where it is to be totally honest, I believe that it's too frail and dependent on team support at times to go to S Rank. Remember it also comes with the cost of not being able to use Mega Heracross or Scizor. Haven't used Staraptor enough to give it fair reasoning.
I'm going to agree w/ AFD that flying should be an exception to the rule. There really are 6+ 'mons deserving of an S Rank and if one was to just go and chose S ranks w/o violating the species clause they would actually come up w/ a team that has all it needs to succeed: Skarm, Zapdos (assuming it goes up), Lando (either form, but therian is better), Thundy, CharX, filler. I know each of us has faced (or used) that exact team on the high ladder or in tours many, many times.
Water is a different story though...
There are 3-4 S ranks that form the attacking core seen on most of the top teams (Greninja, Keldeo, Azu, Gyara). Those 'mons will perform their role for the team w/o much support (I would say Gyarados is debatable as an S rank though). Moving beyond the current S ranks, we're mostly looking at 'mons that form the defensive/immunity core of the team. Each requires support to function effectively or shares a role w/ another A rank, which will make it unlikely for them to move beyond A rank and create a situation similar to flying w/ 6+ S ranks. For instance, it would be really hard to make the argument Lanturn, Swampert or Quagsire deserve to move up b/c a specific one outclasses the others.