I think that when it comes to passive skill checks, the game should announce successes and completely hide failures. Announcing "Failed Perception Check" every time is only going to encourage people to exploit that.
They can purposefully reduce the number of rolls by giving some things automatically *if* you have the skill.
That kinda already exists in 5e with the idea of passive skill checks. That is the average d20 roll of 10 plus (or minus for skill penalties) your skill proficiency.
Passive Perception is already well known and demonstrated in gameplay videos, but you can actually use just about any skill as a passive.
"Because of your score in Animal Handling, you can tell that this type of creature will attack if it feels surrounded."
"Your study of the Arcane arts lets you identify those runes as belonging to the school of Evocation."
"You recall from your studies of Nature that those tasty-looking plants are actually deadly hemlock."
Also, the Inspiration points could be an automatic 10 or 15 instead of just another roll (as seen in one of Sven's gameplays). Rolling a 1 when spending an Inspiration point will piss off players I presume.
So will being stuck with an automatic 15 if you need a 16. It's a second
chance, not a guaranteed success.