Perhaps this will help:
Exactly when to use Investigation rather than Perception can lead to weird cases of seeming less effective because you're actively trying to look for something.
Investigation is for deducing; Perception is for noticing. Investigation is typically when a player is fishing to confirm an assumption or theory and there is some uncertainty on the part of the DM as to whether the character can make the deduction based on the available evidence e.g. "I try to deduce whether these scorch marks on the wall opposite the door indicate the presence of a trap." The player may strongly suspect that is the case, but wants to confirm before taking further action. If the DM decides that it is uncertain the character can make the deduction, he or she calls for an Intelligence (Investigation) check. I think that Investigation comes up more when the DM is diligent about placing clues that telegraph threats or other important elements in the game.
Also, on the topic of "actively trying to look for something," I'm not sure what you mean.
Exactly when to use Survival (most of the time) vs Nature (less of the time) can be odd in practicality, I get that Nature is meant to represent more academic biological/zoological knowledge.
I would say your distinction is a good one. Knowing a thing versus applying a skill set, though it's possible that Intelligence (Nature) can be a "roll-to-do" skill rather than just "roll-to-know" in some cases.
Animal Handling vs vehicles (land). I think a few people were slightly confused by the fact that Ride is not it's own skill, nor is it a tool proficiency. Or rather you don't need a skill or proficiency to casually ride a horse around places.
Right, ability checks are only required when the DM thinks the outcome of a player's stated action is uncertain. There probably isn't a lot of meaningful uncertainty in riding a horse around town whereas in a harrowing nighttime chase on that town's uneven roads might have uncertainty as to the outcome.
I would also say that Vehicles (Land) also only applies to driving carts, wagons, chariots, or the like though which skill applies is largely up to how the player frames his or her goal and approach. I would be inclined to grant advantage to any check related to this if the character has both skill and tool trained.
Performance vs musical instrument proficiency likewise has some blurred crossover.
To keep it simple, any activity with an uncertain outcome that doesn't involve an instrument could call for Performance. Anything that involves a musical instrument could call for the tool proficiency check. As above, I'd be inclined to grant advantage if the character has both skill and tool trained.
In practice though, when DMing I'm happy enough with a player using whatever skill they are better at in blurred circumstances.
I think that's a good move.