You're missing the point with most of these. In almost all of your examples, there's already a rule for how to do something and what kind of action it takes. Trip? Special attack that replaces and attack made as part of an Attack action. BM and monk just modify an already codified rule. Same with AS and cover. Same with many of your comparisons.
But, on most of the ski feat cases, there is no previous codification, rather they lived in the nebulous realm of DM rulings. But, by codification, the DM rulings are now constrained to be at least equal with the expectation of worse than the feat. Acrobatics allowing movement over difficult terrain is a great example.
Also, people are telling you they have a problem. Saying you can't see a problem existing in general is essentially saying you don't believe them. Disagree all you like, but maybe quit assuming the general opinion and instead affirm just your opinion.
People are claiming that there is a problem. My point is that this problem is largely one of your own making and not an actual issue with the game. That you have a problem with these feats is obvious. However, as you yourself admit, the issue is caused because you have extrapolated beyond the rules. Since WotC cannot write rules for your table, but, rather for the game as its written, the problem isn't really with the system is it?
Taking the acrobatics example. There is nothing in the description of acrobatics that even hints that you can use it to move over difficult terrain. What's the DC? How do you even determine the DC other than the, "roll a d20, roll high" method? You've added this, and, additionally, added the idea that you can use acrobatics as part of a move. Again, this isn't even hinted in the rules. Swinging my sword takes an action, but, a series of front flips doesn't?
Hey, it's your game, so, more power to you. Fair enough. But, you're applying your particular interpretations of the rules, that aren't actually IN the rules, in a judgement of new rules and then wondering why everyone isn't instantly agreeing with you.
The PHB is clear, in your turn you can move and take one action, movement can include things like climbing, etc, the DM can tell you to roll Athletics as part of that movement and I don't see why he could not tell you to roll acrobatics or stealth under other circumstances.
A perfectly fair interpretation. However, it's not the only one, nor is it one that's actually supported by the rules. And, while it's fair for your table, it's not fair to assume that your table is the only way these rules can be interpreted. While your interpretation makes these skill feats problematic, another table would have no issues whatsoever, simply because they chose a different interpretation than you.
Stealth can be used with more things than hiding.
True, but, it still takes an action if you want to do it in combat. Which brings me to the next part of your post:
Most skills will be used out of combat where you don't need to control initiatives, moves, actions, bonus actions. In any case in my games the players can control their horses automatically or with a roll of handling animal, move and use athletics, acrobatics, stealth, if they see a symbol while fighting they can roll religion, history, arcana withouts spending an action, they can talk, sing, etc while they are picking locks, fighting, moving things around so they can roll charisma skills without taking an action, perception, insight are also used a lot of times without an action in my table, etc. In my games most skills can be used without an action and the PHB doesn't say I can not do it.
Too true. It's very true that outside of combat, there is no Move/Action economy. You simply do whatever. Fair point. But, also very much besides the issue. Since we're discussing feats that allow skills to be used in combat situations, saying that you can use them outside of combat is not terribly helpful.
However, fighting in particular is pretty hard to do in D&D outside of the action economy and very much outside of the scope of the rules. Perception in combat is specifically an action, as another example. And, in fact, the PHB very much does specify that performing certain actions during combat are very much subject to the action economy.
Again, WotC cannot write rules for YOUR table. And it makes it very difficult to carry a conversation when the rules are subject to the caveat of "well at my table" at every turn. I don't play at your table, and you don't play at mine. I'm telling you flat out that at my table, these feats are a complete non-issue. None. They do not cause me a second's pause, and, in fact, at the end of today's session, the group just hit 4th level and three of the six players took either skill feats or racial ones. THAT'S how little of an issue I'm seeing here.
Why am I not seeing a problem? Because the interpretations of the rules that I've made means that these feats are a complete non-issue.