Recently reached 1500 elo with a team that doesn't use Snorlax, so I think I have a unique perspective on this.
(Proof:
https://replay.pokemonshowdown.com/gen1ou-1671958287)
S:


A:


B:


C1:




C2:



D:





(unordered)
Chansey is the most indispensable of the "big 3," and in my view, at this stage in the meta, slightly edges out even Tauros. It's the only Pokémon in the game that is straight-up
buffed by being paralyzed—that is to say, the benefits of getting your Chansey paralyzed utterly eclipse the downsides in a manner that may as well be referred to as a "buff," because that's essentially what it is. There's a reason many people will forfeit the moment their Chansey gets frozen; without Chansey in play, it becomes almost impossible to protect the rest of your team from status conditions in a meta where inflicting status serves as your primary win condition. I would liken losing your Chansey in RBY to hanging your queen in chess. It's a tremendous setback that is extremely difficult to come back from, and not having a Chansey on your team while your opponent has one is like being 75 meters behind in a 100 meter dash. It's that important. The choice to forgo Chansey on any serious team can only be described with one word—foolish.
Not much to say about Tauros—it's still indispensable, and the king to Chansey's queen, but its vulnerability to status conditions and inability to recover its health means that you REALLY have to pick your battles with it—a downside that Chansey lacks. Chansey can safely switch into every special attack in the game when paralyzed. Tauros cannot. That said, obviously, it's still the best kill switch in the game. I think people will always view Tauros as #1 because of its role as a sweeper—after all, Tauros is designed for scoring KOs, and Chansey isn't—but the thing is, Tauros needs a lot of support before it can get that late game sweep going in the first place, and Chansey is simply the best Pokémon at providing that support—and, therefore, the true MVP of the metagame.
Snorlax is overrated. As I mentioned above, the fact that I was able to reach 1500 elo
without a Snorlax basically proves this in my eyes, especially when I didn't find the task particularly difficult. It goes without saying that Snorlax is strong, and can be a challenge to deal with—if you don't have one yourself, it's probably gonna take more than one of your Pokémon to deal with it (unless you run Porygon). However, Snorlax has a bevy of exploitable weaknesses that simply prevent it, in my eyes, from being the true undroppable S-tier Pokémon that everyone seems to think it is. For one thing, it gets outsped by Chansey and Rhydon. Any Snorlax that switches in on a healthy Chansey puts itself at risk of getting hit by all manner of status conditions. Since low speed means bad crit rate, Chansey is very likely able to take at least two hits before needing to switch out, which means that Snorlax has to dodge Sing three times in this scenario before its opponent pivots to another, more accurate sleeper. Snorlax is one of the worst Pokémon to have asleep or frozen. Rest is annoying to deal with, but the fixed two-turn wake up makes it extremely easy to exploit the wake up turn and simply put it back to sleep, or even just smack it with Alakazam Psychics until it dies in two or three hits (minding his high crit rate). Without Amnesia, it also struggles to deal with Porygon, which is just... kinda pathetic, really—and with Amnesia, you're running a suboptimal Snorlax that's even easier to exploit. Obviously, I'm not saying Snorlax is trash—I have it at the top of my A-tier, and it's still the third strongest Pokémon in the meta. But this notion that you can't make a good team without one is just utter nonsense. It is by far the least threatening of the big 3, and I think its popularity is more a measure of self-reinforcing groupthink than anything else. "It's true because the community says so," or "It's true because the numbers say so," rather than "It's true because you literally cannot win without Snorlax." This isn't GSC—you CAN go without Snorlax. It's just a very strong Pokémon that you probably
should use. Nothing more.
Exeggutor is extremely annoying. Like, nothing kills it. Even moves that are supposed to kill it (Starmie's Blizzard) do a terrible job of killing it, and even then, it has such an easy time putting all its checks to sleep anyway. The only surefire way to KO an Exeggutor is to have it blow itself up—a scary prospect, which makes every encounter with this big dumb palm tree far more of a nail-biter than it ever feels like it needs to be. In my opinion, every team needs to pack a Rhydon, a Gengar, or both, simply because of this Pokémon alone. The only reason it's not higher than Snorlax is because when it blows up, at least it's gone for good.
Alakazam and Starmie are incredibly strong, but they're down here because they are absolutely terrible at fighting other special attackers, including themselves. An Alakazam cannot consistently close the deal on another Alakazam, which is a problem. Starmie has Thunderbolt to deal with members of its own species, I suppose, but Starmie's problem is having to run Thunderbolt in the first place when it would much rather be running STAB. Out of all Pokémon in the RBY meta, Starmie suffers the hardest from 4MSS, and it's a shame to see. I would also like Starmie more if it had a little bit more HP to supplement its decent physical bulk—but then, it would be even harder to two-shot it in the mirror match, I guess. Oh well.
Rhydon is good enough that I believe every team (at least of certain archetypes) needs to use it, but HAVING to use Rhydon also kinda sucks. Getting walled by Pokémon like Exeggutor and Cloyster blows, and moves like Rock Slide simply aren't strong enough (or accurate enough) to consistently deal with these threats. Plus, since Subsitute is garbage in this generation, it's liable to getting checked by all sleepers, as well, since they all outspeed him. Even Chansey can two-shot it with Ice Beam. Rhydon has a lot going against it, making him one of the harder meta Pokémon to use, but he's an absolute beast if you play him very intelligently.
Jynx is basically a less scary Exeggutor that gets STAB Blizzards and freeze immunity. Too bad it doesn't have the same bulk, and only runs three moves (nobody has ever seen Jynx use its fourth move. Ever). Cloyster gets the same Ice-type benefits, but of course trapping, while extremely annoying, is also super gimmicky and inconsistent.
Slowbro spends too many games dying before it can get all of its boosts up before it's able to wreak any real havoc, but it can be scary if you're not prepared for it, or if all of its checks are dead (which means you're in a pretty bad spot anyway). The problem is, even if its checks are crippled with status, they can still deal with Slowbro adequately.
Gengar would be C1-tier or higher if it had a better sleep move, or a slightly higher Attack stat, or wasn't weak to Psychic, or wasn't weak to Ground, or had ANY good STAB moves, or if Mega Drain had a higher base power, or if the most common leads in the game couldn't threaten to OHKO it, or if it wasn't speed tied with Tauros, or if it had any sort of consistency whatsoever. It really has everything going against it in this generation, doesn't it? The fact that it's usable in the meta at all is actually incredible. You could fix just ONE or TWO of those issues I mentioned, and Gengar would be an excellent Pokémon, all for the sheer utility of its Ghost typing alone—but to have all of those issues at once? It's just... a lot.
Jolteon gets to be in C because it's the fastest viable Pokémon, and it's capable of slapping Chansey around in a pinch. It has some respectable characteristics. I just don't care about Electric-types in this meta when you can just run Rhydon and shut them down completely. Zapdos gets to be much higher because it's much bulkier and Drill Peck is very strong, but it's underwhelming for the same reason. It's too bad moves like HP Ice and Roost didn't exist yet.