I think, gentle reader, that by now we have some understanding.
I do not like D&D’s core 6 stats, and I am suspicious of its choice of skills.
The stats are distributed such that certain archetypes overload in odd ways (clerics; trapfinding).
The skills prohibit direct weapon skill (laudatory) but then immediately sink back into problems when they get into grappling and the hide-and-seek game. Oh, and the social skills aren’t to my taste.
Time for fixes!
Not of the stats; my problems there are well known and I think I’ve sufficiently covered my bases.
For the skills.
1) Drop the investigation, perception and, possibly, insight skills. You can still call for these checks; they are lore-ish skills combined with the appropriate stat for the check (dungeoneering underground, nature in the woods, streetwise in a city, etc) adjusted by wisdom to spot a detail and derive data. A character may request +int instead for a check performed over a long period, or +cha if the check is in conversation with a creature.
The DM determines the appropriate skill and it’s generally obvious — based on what the scene appears to contain. If its a complex scenario (can you tell that the beautiful maiden — diplomacy or history — is actually a wicked hag — nature?!), the DM can either explicitly list the available skills, somewhat tipping their hand, or see the next part.
2) Spot something or suffer isn’t a good use of the skill system. When you get down to it, things like ambushes and ruses are traps, and should use trap rules. At the point where you’re determining surprise, don’t make a skill check.
Make a saving throw.
Now, there’s a problem here, which is that wisdom is overloaded to willpower, and this really wants to be a wisdom save. You can get around this by making it a dexterity save, or you can make a new category of saving throw, “surprise save”, based off of wisdom, which rangers, druids, fighters, monks, rogues, elves, halflings, felines, serpents, dragons, and any creature with any form of sharpened senses are proficient in. This is what generally opposes stealth in combat.
Failure means you’re caught by whatever nasty surprise you had hoped not to be, which is generally a brief effect followed by more saves for everyone. The brief effect is often called “surprise”.
This solves the case of the sweet-presenting hag; if characters interact with her they can put forward their suggestions of what she is and bring their skills to bear; at the last minute if they haven’t pierced her disguise it’s unmodified surprise saves all around at the moment the cat’s out of the bag.
This also solves the ambush problem; players can interact and detect things using the appropriate skill, but will ultimately fall back to a surprise save at the last minute. Same with dungeon traps.
3) Grapples. Grapples use the skill system because they’re a canonical example of freeform resolution, inflicting a condition in exchange for going off-book. Unfortunately, they also unfairly privilege the athletics and acrobatics skills; why should rogues be better grapplers than fighters? And so: I move grapples back into the combat system.
Making a grapple is considered a strength-based martial weapon for proficiency; it targets not armor class but a dexterity or strength save. Monks are proficient in it also. Escaping from a grapple is that same strength or dexterity save. Magic that affects skill checks (guidance?) need not apply; magic that affects saves is fine for defense, and magic affecting offense affects the initial grab attempt.
This constrains the role of skills to active use by the player, which is good because passive use should be a save to prevent a specific bad outcome. This also constrains skills away from defending against particular combat moves — valuable because of the common nature of those moves. Finally, it makes grappling a sort of specialty weapon, which better matches its use.