You have this habit of thinking that because I disagree with you I must not have "optimizer's eyes."
You are wrong. I can disagree with you even though I do have the ability to optimize and recognize optimization.
Because what we disagree on is not the effect of the combination of factors that go into the optimal scenario, but that a single one of those factors can be ruled as over-powered because of the performance of the entire combination of factors - because those other factors (buffs, for example) are not an inherent part of the single factor (the feat).
This is exactly the core of the issue.
I am claiming that, yes, by itself, a feat like GWM isn't terribly overpowered. That is what I mean when I'm saying that as long as you can't mitigate the -5 part, the +10 part isn't unbalancing (except in corner cases, which we can ignore).
But the reaction I expect from that isn't "okay then, so nothing wrong, let's move on".
The reaction I expect is "interesting, how often and how easy is those mitigating factors to come about?"
Because that's my point. The designer of the feat failed to realize how many and varied the ways are to make the -5 part go away, either in full or in part. This in turn makes the feat useful in too many situations, against too many monsters.
In essence, the core balancing question (that is never discussed IIRC) is:
What AC cut-off point was the designer gunning for? (I know this is a moving target, slightly moving upwards as the character levels up; I believe the math analysis pegs the cutoff at whatever AC you hit when you roll 8 on your attack die).
But bear with me as I attempt to illustrate.
If (and that is merely speculation) the feat was designed so it would only provide most of its benefit* against AC 10 or lower foes, then it would probably be quite alright (or even woefully underpowered, but lets leave it at that).
A naive example is Strength 18, proficiency bonus +3, and the full -5 penalty. This means you need to roll 8 to hit AC 10.
But if the feat turns out to provide most of its benefit against AC 15 or below, then I hope we can agree it is overwhelmingly impactful. As in "the average player can reasonably expect a significant portion of the foes she will face will sport AC 15 or less".
A more realistic example is Strength 20, proficiency bonus +4, and the penalty reduced to -2 on average. This means you need to roll 8 to hit AC 15.
And if the feat is in play in a high magic campaign, providing a benefit against AC 20 or less, then it should be clear to everyone its damage boost is off the charts. The feat is utterly broken in this scenario - as in there is no other combat feat providing even remotely the same bonus.
Now we're definitely leaving the kindergarten behind. In this example we sport Strength 22, proficiency bonus +5, another bonus of +2 and the penalty reduced to -1 on average. This means you need to roll 8 to hit AC 20.
The sad part is that this last scenario is not some far-fetched improbable monty haul kind of fever dream.
Many many campaigns at double digits will get there, just by playing the game normally. The +2 could come simply from a +2 weapon, but there are (as I'm sure you will agree) many other ways to gain such a benefit. The penalty reduced to -1 is actually generous, because a bit of it is still there. In reality there are bonuses that add much more than a mere Bless 1d4, and it comparatively easy (especially at that level) to combine two or more effects such as advantage plus bless.
As for the Strength 22, you might be ready to decry, say a Belt of Giant Strength as the real culprit. But again, no, the real problem
is the feat. Yes, the belt adds +1 +1 on top of what's normally possible, but that is in itself not terribly unbalancing. It is the compound effect of raising the feat's cutoff point to AC 20 that is the real culprit here.
Besides, you can gain a Strength 22 in other ways. And even if you absolutely will not accept that Strength 22 can occur in a "normal" campaign - fine, then the cut off point stays at AC 19.
That is still way too high. That is still way higher than the designer must have foreseen.
*) By "most of its benefit" I mean, that against the very AC that is its cutoff point, there is no problem, since the dpr increase (compared to not using the feat) is barely positive. But if that AC cutoff point is too high, it allows a too-wide spectrum of foes where it is not merely good, but great, or even wildly powerful.
Now, I maintain that while the feat itself might be designed for a reasonable AC cutoff point, the designer failed to take into account all the varied ways of increasing that cutoff point (sometimes drastically).
That does not mean that those "ways" (bonuses from spells, items and class features) are themselves unbalanced.
Because the real problem is the feat. The feat represents a too-great damage output to elevate by those other "ways". There are few or even no other ways to use those ways to add so much damage to each and every blow you make.
It is clearly
the feat that is the source of the problem.
You can't add ten points of damage to a feature (an "attack) that normally deals only that much damage, that's a 100% increase. The designer evidently thought the -5 part would keep that under control, but then he or she failed to account for player creativity and cunning.
What other martial character? There is no guarantee of their being any other martial character in the party, nor of another martial character that happens to be in the party having better damage - so again I ask, Outdamaged by who and why does that matter?
Which is exactly the thing I've said to you numerous times so far - that something not working appropriate in one of our campaigns doesn't mean it won't work appropriately in another, which I acknowledge when I say things like "seems to be working as intended" because the thing can work without alteration, when you say things like "is broken." because it doesn't work appropriately in your campaign (and then rudely insist that anyone whose campaign it works in just isn't looking at it with the "right" eyes.)
Also, I used the phrase "keeping up" not because the rest of the party is doing roughly equal portions of the damage, but because the barbarian is keeping up enough damage that it isn't out of place to refer to him as the party's "go to damage dealer." But I can see why one would assume the other usage as you have done.
Let me adress the "what other martial character" bit:
I am saying the feats' biggest issue is that it steers players towards build choices involving greatweapons and ranged weapons, because that is the only two weapon groups that can be used with -5+10.
What is so hard to understand about that?
No, if everyone else is a spellcaster, then the biggest issue with the feats never comes up. So what? Just because it no longer is an issue in your campaign does not mean it ceases to be a general problem.
Again, the most clear and direct way of explaining the problem is to visualize a group where two players want to play an offensive fightery person. Without feats, the difference between the barbarian with a greataxe (say) and the ranger with sword and shield (say) is nicely contained - one does a bit more damage, the other has a bit more defense.
But when you add feats, all of this is thrown out of whack. Because suddenly one character (the barbarian in this example) will start doing damage leaps and bounds above the other one. For a player with at least a nominal interest in the "game" part of the session, that is, a player not oblivious to his character's effectiveness, it no longer is excusable to abstain all that damage.
The feat reduces choice, since with the feat you become so much better at your fundamental job, which is to deal damage. Not just a little better, but too much better.
So asking questions about exactly "what person is this" is completely missing the point. The answer is simply "anybody that's trying to be a fightery character but not taking those feats will regret that choice if playing in the same group as somebody that did take those feats"