Im starting to split ends here, but doesn't this also apply to Freeze and Paralysis? As opposed to the 1-3 turns of nothing, which can be mitigated with moves like Sleep Talk and Snore, you cannot do a thing about being frozen. You're stuck there, actually incapable of doing anything because the opponent got lucky. Or, Paralysis, where it's quite easy to proc and results in a permanent speed debuff and a random chance to, wait for it, not do anything. So why is Sleep any different? If anything, it seems that a guaranteed removal of the debuff one to three turns later is better than being permanently frozen or paralyzed, but thats just me talking.
I would say Freeze is in the same realm of critical hits of "there's nothing we can really do about it" - its very difficult to isolate and prevent without modding the game, and with a few notable exceptions it's quite rare. In fact, I'd say just one notable exception, Kyurem, which honestly should be suspected. But overall, like critical hits, it's just part of the game that we can't do much about save for banning all ice moves, which at that point why not ban all moves that can crit?
And I've got my thoughts out about Para already, it certainly falls under the realm of RNG fishing but the player using it has much less control over this than with sleep (you choose when to put someone to sleep, you don't choose when para activates.) Rate of activation also matters a lot with this control in mind. 100% then 67% chance of an immediate free turn is much more significant than a 25% chances of potential free turns at some undetermined point later in battle. And there is nothing uncompetitve about lowering a Pokémon's speed. Overall, paralysis still maintains a good deal of agency for the paralyzed player in a way sleep does not, save for your suggestion, to put Sleep Talk or the fake move Snore on random Pokémon that don't have Rest, which is pretty much the picture of a consequence of overcentralization and amounts to a canary in a coal mine similar to running Bronzong to counter Bloodmoon or Dachsbun to Chi-Yu.
I think a whole lot of headaches, strawmen, and whatabouts can be saved here with the framing "sleep introduces an element of RNG fishing and loss of agency beyond what is acceptable or standard"