Not your screen monkey (he/him)
Indeed. And played who are good at the improv and interaction are going to find cases where the approach they take is SO reasonable that the success/failure isn't really uncertain, just like the player who's good at tactical combat is going to work their feats and abilities that synergize with other players' abilities and spells to make combat easier.Remember that D&D 5e specifically says that the DM first determines automatic success/failure, and only if it is "uncertain", and there are consequences for failure, should an ability check be called for.
So, sure, sometimes the DM should listen to that silver-tongued BS artist and still say, "Ok, give me a Charisma check, DC 15."
I mean, ultimately it comes down to whether your trust your DM to make good calls, or if you think he/she is going to let Frankie always get his way, while penalizing Susie for not being as glib. And if that's what you think of your DM, find a different one.
But in both cases, when there's uncertainty, they are going to roll no matter how glib Frankie is compared Susie.
The fact is, if someone like Frankie is a lot better at those aspects of the game than Susie, if I just valued skills and adjudicated based on player skill, he IS going to be a lot more successful than Susie in uncertain situations. And that's why I don't do that and, instead, tend to rely more often on the die roll in those cases - and thus the character's assets more than the players.