The problem I have with your variation is that it's not explicit on how the player wants to resolve the situation. Sure, they want to talk...but there are several skills which cover "talking". Without specifying, I've been at tables where saying "I want to try to talk things out." gives the DM room to say "Oh well, that one skill that nobody in the party has? Yeah that's the talking skill you need."
Well, we're adult people in a social game -- if there are questions on approach, we resolve them. It's not anything like a "You said it, and now nothing else can be said." But, yeah, I guess if you have a gotcha jerk as DM, your last bit there might be a problem, but I'd rather just not play with that DM.
By specifying which skill they want to use, they're specifying how they want to resolve the situation, how they want to frame the talking. Are we big tough scary adventurers intimidating our foes? Are we suave smooth-talking criminals with a silver tongue? The player is deciding how they want to frame their attempt by naming the skill they want to use, instead of simply reacting to DM scene-framing by rolling whatever check the DM says is necessary.
Again, you miss the point. The player is still deciding how they engage the framing, but instead of going straight to mechanics they just naturally say what they want to.do. If the DM thinks that works without a roll, then it works, no mechanics needed. Only at the point a declared approach is uncertain are mechanics engaged, and they're engaged unsung the player stated approach, not a predetermined DM skill check.
And really, you're not going to reduce "skill-naming" by giving out DCs like that. It's just going to make the players reactionary. Oh there's a DC? I can roll for that.
The DC isn't given until the roll and stakes ate set based on the layers declared action and approach, so, again, you've missed the point.
When a player tells me they want to talk things out, my first response is "How?" then they'll usually indicate if they're going to use honey or vinegar and if they want to actually role-play what they're saying that's great and then I'll roll behind the scenes for how well their attempt was received.
Right up until your roll begins the screen is what hastens at my table. I don't roll dice for my players, though. If it's uncertain, they roll, and success and failure are clearly set.
There's no point in actually having skills, in doing the work to math out skills, in writing down all your skills if your DM is just going to tell you to turn your sheet upside down. You need to know what skills you have and you need to know when you want to use them.
Is it really so hard for a player to know that they have a good persuasion score to declare actions that frame advantage of that score without says "I roll persuasion!"? How the player forms action declarations is up to them. If you imagine your players turn stupid ou'd the can't just name skills on their character sheet, that's on you.