Different pokemon probably have different capacities for speech. In the anime canon, Rocket Meowth pretty much fucked his entire development as a pokemon to be able to speak as a human, so he can't use Pay Day and likely will never be able to evolve (thats the theory Maddie Blaustein, his main VA, had for him anyway, and it explained why he's so jealous of Persians)
Meowths are a rather intelligent species which gives them the potential to pick up human speech, even at such a cost. Slowking is another anime species that is known to be able to speak, and also highly intelligent.
In Sun/Moon there was a Mimikyu that spoke in broken english about cursing you, so there's one in the games as well. All in all different pokemon will have different capacities for speech, and more intelligent pokemon are more likely to be able to pick it up (or just use telepathy)