Its all ability checks anyway so let players create their own skills and apply them to whatever stat role role can justify.
In a sense, that's what 5e is about. This is why there are few skills and why each character has few of them. It's basically just an ability check and in a few cases a skill applies.
I like that idea just from a "character sheet as menu" philosophy of DMing.
I'm thinking more about some of the differences I'm noticing between how types of skills / checks work at my table. Knowledge checks and Perception/Insight/Investigation checks are examples, but the one at the forefront of my mind right now are Charisma checks involving Deception, Intimidation, and Persuasion.
What I notice among my players – and this is not just my players who onboarded during 3e, but even strangers relatively new to the game who I've been running one-shots for – is that they ask to make Intelligence-based and Charisma-based checks more often than they ask to make other checks like Athletics or Stealth. With those more action-oriented skills, it seems to be rarer for players to interrupt that engagement / flow to say "can I make a Stealth check now?" In other words, they're much more comfortable waiting for me the DM to call for the check. Whereas, more often my players are the ones beating me to the punch asking, "Can I make an Arcana check to see what I know about the orb?" or "Can I distract him with Deception or Performance?"
Do other DMs notice that trend?
It's really interesting to me. What if for Charisma checks to influence NPCs I flipped the script so that instead of 5e's baseline assumption that the DM calls for the check, instead the player proposes the check? And what if part of that proposal involved agreeing with the DM on what happens on a failed check? My idea is to harken to the old school sentiment, "if you can avoid rolling with clever play, avoid rolling." So instead of players jumping for their dice, the style of play would be the player RPing to see how much they can convince the NPC before coming to a social loggerhead point and really wanting to make a check to breakthrough it. For instance, maybe they can lean on something they know about the NPC or have over the NPC to avoid the check altogether (or, another way of saying it would be gain an auto-success). This would build tension, as in...
Oh man, I really want to Persuade this guard to let us pass right now, but I can't think of anything to say to convince him, and can we risk the fallout if I fail my check?
Examples of fallout for a failed Charisma check might include an increased risk of hostilities, a lower returns on rewards, an inability to network, being denied access to an area, popular sentiment in that area/among that group turning against you, being elevated as their deity-to-be-sacrificed, and so forth. Probably to flesh it out, I'd pin down a couple examples of fallout conditions for each Deception, Intimidation, Performance, and Persuasion.
So instead of something like Stealth, where you need to take action (e.g. get behind cover or turn invisible) in order to attempt the check, with this approach to the Charisma skills, you can
always attempt the check
but doing so requires articulating what the consequences for failure will be. This regulates how often the players are going to be willing to take that risk, encouraging them to ask for Charisma checks only when they're really invested or really need it.
EDIT: Maybe even some kind of risk vs. reward system, where the higher your Charisma skill value, the more you can raise the stakes for better rewards along with more dangerous risks.