we already have plenty of sources of exp (arguably maybe even too many, as we are leveling up at a very fast pace).
I am conflicted. There is a lot of content packed into the single act we are given, and I reach level 4 maybe 20% of the way into and spend the rest of the act "capped," but I also go around and completely clean out any and all encounters. In one of my saves, I actually collected every single plate, crate, box, cup, etc, and organized it in my camp.
If I were more inclined to hurry to my goal (I'm not, which is sort of a problem in and of itself, but that's another topic), I'd very likely level much slower. I wouldn't find as many encounters, I wouldn't talk to ANY NPCs beyond those I have to. For people who want to go around soaking up all that experience that the world is rich with, I don't see any reason why they couldn't.
A solution to the abundance of experience sources would be an increase in difficulty regarding the day-to-day living and recovery. Free rests and instant travel with no time constraints means I have no reason to hold spells, carry food, conserve consumables, and so on. No one will chance upon my camp and steal my stuff, no one will pick my pockets and take my money, and even if my character never eats, they will never starve, so I have no reason not to just leave tons of loot in a barrel at my camp.
If long rests and travel actually used up my time rather than being 10 second cutscenes and instant travels back to my camp, I wouldn't use them after every encounter. If I only had so much food, I'd be less willing to spend days in search of experience. If food didn't restore hitpoints, I'd have to source some healing from spells, potions, scrolls, or wands.
you may want to reconsider the idea of rewarding the grinding of every single trap on your way, rather than the ability to reach a certain goal. Otherwise you'll end with something like Deus Ex (human revolution) where getting the password for a computer was sub-optimal because you were still rewarded more exp for hacking it manually anyway.
It's worth noting that you could make opening the door what rewards the experience rather than picking the lock. If you found the key, bashed it open, or convinced someone to open it for you, you get experience. If you convince a party of enemies not to attack, you get experience equal to what they'd be worth if you killed them. If you kill them afterwards, you get no experience, because you already 'defeated' the encounter. The experience being awarded is for completion of a goal, as you suggest in your edit, rather than a particular action or kill that yields the experience.