I generally think rule for specific skills generally tend to discourage players to try to solve puzzles. If you link non-combat actions to skills, you generally get these problems:
1) People don't attempt something unless their skills are maxed, so attempts to think outside the box are generally shut down hard.
ie. "I want my barbarian to creep up to some guards and clunk their heads together." Sorry, you don't have stealth trained so they'll probably see you, and you'll never train in it because you'd have to be worse at what you can do and are expected to do to fulfill your party role. This is especially bad when your class doesn't give you many skill points.
2) Exclusive skills generally tend to mean that characters do non-combat actions apart rather than together (ie. Stealth). If you can get help from your friends when doing combat, but you are stuck all by yourself trying to skillfully solve a situation, is it any wonder players try to carve their way through everything?
3) Skills can often replace problem solving rather than encouraging it. I've already spoken often about how "Diplomacy" becomes a magic "I win, do what I say button" without any roleplaying support. But the case can be made for any skill that it discourages looking at each situation carefully and trying to figure out the best way forward.
So I picked the castles and crusades option in the poll.
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For 5e, I definately have to think about this. It reminds me a lot of how 2e NWP were used in actual play (at least in my groups). In 2e you got so few non-weapon proficiencies that no character could possibly function on just those few specialized skills, so generally it defaulted to ability checks anyway. Thus there was no particular reason to have proficiencies on your character sheet except to remind you that you knew herbalism, or could brew beer, or you could train horses. If you needed the party to ride across country, you still allowed them to ride cross country even though only one of them had the ride proficiency (using dexterity or constitution checks).
The thing is, those reminders were very useful, and was something that the 3e/4e skill system (being very broad and general) tend to discourage specific applications of the skills. You could use perception to read lips for example, but I've never seen anyone try to read lips in the 12 years since 3e has hit the shelves.
So if you have a Wisdom (+4 read lips) skill system, I think simply having that bonus on the character sheet will encourage the player to read lips. So I think this is pretty much a better implementation of the non-weapon proficiency system than we got in 2e.