I don't really care about deliberating on what "is" broken or not broken. As this thread and other discussions have shown, it all comes down to arbitrary opinion in the end. I would certainly agree that a lot of Smogon's rules are, to an extent, arbitrary and even inconsistent. On the other hand, arbitrariness in a ruleset as large as Smogon's is pretty much inevitable. We're always going to end up banning movesets and tactics that are not broken in the slightest. So I'd say, forget about all that. I tend to agree with the side that looks the most practical to me, not just in terms of playing the game, but also in terms of being reasonably enforceable on cartridges, easily implementable onto a simulator, and easy to get into.
Treating a Pokemon as a unit has many practical benefits. With Team Preview, you can immediately tell if an opponent is breaking one of the rules. The exceptions tend to be stuff like evasion and the Drizzle + Swift Swim combo ban. And this is where your analogy to government nitpickers actually works for their existence. Pokemon-as-a-unit is not a hard and fast rule that we defer to no matter what. Drizzle is a team supporting ability, and Swift Swim is on several different Pokemon. The combination resulted in a broken team trope. The combo ban is the most efficient, practical solution to address this specific issue (other than maybe just banning Swift Swim). Unbanning Mold Breaker Excadrill and Blaze Blaziken does not have nearly the same practical benefit as the Drizzle + Swift Swim combo ban.
Slippery slope is not inherently a fallacy. It is a fallacy if it isn't justified, and I think in this case it is. I recall Philip7086's ruling that we should strictly adhere to in-game mechanics and availability (which we now only break with Sleep Clause, again for practical reasons). Despite the Policy Review voters deciding against adhering strictly to game mechanics, obi / david stone came along and demonstrated a potential consequence of not striving to adhere strictly to game mechanics. It wasn't so much that we would try to remove critical hits, but that there was honestly no reason not to do so without deferring to adherence to game mechanics. I don't think anybody likes crits and what they do to the game overall, but we deal with it now precisely because of adherence to game mechanics. I see this as the same deal. It's not so much that we would try to do the same thing with other Pokemon, but that there isn't much of a reason not to do so without deferring to a general agreement to treat a Pokemon as a unit.