Sigh. This comes across as grasping at straws to avoid having agree Paizo's design is (much) less than ideal.
Eh, I’ve been pretty forthcoming here about my dislike of certain elements in Pathfinder 2e. I don’t like skill actions at all. I think bringing them forward from Pathfinder 1e was a mistake, and they could have retained the degrees of success approach with something simpler to use and adjudicate. I just don’t agree with you regarding the problem skill feats purportedly create.
Okay, let me agree that there can be other approaches that are bad and even just as bad. That is, let's not make this out to be "your idea is bad too so PF2's system isn't so worse off".
In other words, you are skipping all the other criticisms I have, and you zero in on just "your suggestion can create complaints too". It's hard to not interpret that as trying to wriggle out of my rather massive criticism against the PF2 implementation.
So. If it helps, consider me instead saying the feat gives you a reroll (aka advantage) if that makes you feel better. And this is definitely not limited to just Make an Impression.
The only difference between what you’re suggesting and what we’re suggesting is that your approach explicitly enumerates the trade-off instead of leaving it up to the GM to decide. If I say, “you can do (some activity) with a cost, and the feat lets you do it free,” and you say, “the rules let you do some activity, and the feat gives you a bonus while doing it,” what’s the difference? The cost has been shifted, but there’s still functionally a cost. The only difference is in how it’s accounted.
I'm talking generalities. Just about every skill has several use cases that feel incredibly constrictive and artificially limited, and then you realize that is to justify adding a feat to the game that lifts those weird restrictions.
That’s the problem. Whenever we start digging into details, the criticisms don’t hold up. Maybe a few feats are bad, but a few bad feats don’t show a systemic problem.
The way PF2 prohibits the generic character from doing things at all, unless she has this or that very specific feat, is really really annoying game design on so many levels.
That’s only the case if you take it that way. I don’t think the system necessitates running it the way you claim it does. If you let someone do something at a cost, and a skill feat lets them do it for free, you haven’t invalidated the skill feat by your affordance. Yes, maybe now it’s less valuable in a strict sense, but if the game is more fun for everyone, then isn’t that a good thing?
On the other hand, if the players hate that and prefer you don’t do it, then where’s the problem? They don’t want you to be a permissive GM. They want you to take a very rigid approach to adjudicating the system that preserves (though I would argue increases) the value of their feat choices. Maybe it makes for a miserable experience, but that’s what they asked for and received.
It means players must carefully comb through all the rules and all the feats. Restrictions are not highlighted or spelled out. It's very easy to just assume you can do stuff and then be told you needed to take a feat available at level 1. There needed to be giant exclamation marks all over the place cross-referencing each weird limit with its absolving feat(s):
"please realize you can only crawl stupidly slow unless you pick Quick Crawler"
"please realize you can't climb with a weapon in hand unless you pick Combat Climber"
"please realize you can only jump hilariously short distances unless you pick Cloud Jumper"
This stuff is simply not mentioned in the sections on crawling, climbing or jumping.
It does tell you.
Crawl tells you how fast you move (5′ in one action).
Climb indicates in its requirements you must have both hands free.
Leap and
Long Jump tell you how far you can jump (Leap up to 10′ and Long Jump up to your speed based on the DC). Again, that’s how exception-based design works: you follow the general rule until you something brings the exception into play (a feat, a spell, the GM, etc).
...the list goes on and on, and is probably growing with each new splatbook

Every single little aspect of pretty much every behavior feels carefully combed out "how can we squeeze seven feats out of this simple action?" That is just a question no game designer should ever ask themselves!
The same issues surface on the other side of the GM screen. I would guesstimate that as a green PF2 GM probably two out of three times I tried being a good GM that say "yes" or "yes but" by allowing people to cut corners and avoid weird artifacts of the system (anything from jumping across tables to reaching that one extra square to open a door without spending a whole extra move action) I will later be reminded by a disappointed player that I just gave out for free what a whole feat is about. Using Recall Knowledge on tracks you find in a forest. Using Intelligence to gather gossip in a village. And so on and so on.
Are you talking about
Survey Wildlife? I’m not sure which feat you mean by the gossip example, but it’s my understanding the designers consider it bad design for a feat to change which ability score an activity uses (so that would be a bad feat). Regardless, I agree with you here on Survey Wildlife as well as on whatever feats would let you change the ability score (becuase that’s supposed to be bad design).
I think that should be implicitly part of the Survival skill that you can identify the local wildlife and make an appropriate Recall Knowledge check about it. I can see ways of adjudicating that activity that would avoid invalidating the feat (make it take an hour or a day), but this is a case where one does need to know about the skill feat to make rulings, which shouldn’t be the case normally. I agree that’s
a problem, but I don’t agree that it reflects a systemic one.
Personally, I’d probably just get rid of Survey Wildlife or change it. It’s a bad feat because it has you roll twice, which is an example of
rolling to failure. It makes more sense for the general case to roll twice and the feat to let you roll once or to roll once and for the feat to give you a bonus. Again, Paizo dropped the ball with this one, but I still don’t agree it represents a systemic issue with Pathfinder 2e.
Simple obvious stuff that Paizo is sending a clear message to stop doing: "Don't just allow that, we have created feats the players need to take!"
It is a really really frustrating game design, dead set against the very goals Paizo is professing to have for their game.
Given the amount of disagreement on this point, it doesn’t seem like the message was as clearly sent as you say.