That's not an issue with the aiming mechanic though. That's more of an issue of how character models interact with cover that runs contrary to how most modern tactical games use cover. If you think about it, PP's treatment of cover is closer to X-COM; the best way to not get shot is not to be seen. It is still nonetheless frustrating to see a triton sniper score a head shot against a trained soldier who should really have an animation to actually use high cover instead of just standing there.
There is an animation with low cover, at least; character models will crouch behind it, so ironically low cover actually is a little less annoying and probably more effective to use than high cover.
The aiming mechanic itself is fine and adds a fair bit of tactical flexibility to the game.
The reason it's related is because most games (including Xcom) determine cover using tiles, if your character is on the right tile, you're in cover, regardless of their animation. Because Phoenix Point decided to implement their "aim at enemies" mechanic, they had to instead use a system whereby cover is based purely on how visible you are. In a tileset based game, this is horrendous. Even in a "free movement" game like Warhammer 40k, this is horrendous.
So yes, this IS the aim mechanics fault. It has affected the rest of their game design, and it looks like it did so in a really bad way.
Which still has more to do with poorly implemented animations to cover this eventuality than an inherent fault with the aiming mechanic itself.
If the soldiers had proper animations where they actually used high cover, or even just an actual crouch, prone or change facing button (hell, even Phoenix Point's "cousin", UFO Afterblank does that, and that doesn't even have a cover system) then there wouldn't be that much of an issue.
If standing behind high cover would completely make your character hide, then the only times you'd be able to shoot them anyway with free aim would be "cheap shots", making the aim mechanic pointless and frustrating for everyone involved.
You can't have it both ways. You can't complain that people won't go into cover but then propose a system where they DO actually cover themselves and then cover works properly, undermining the aim mechanic.
If a character can completely cover themselves visually, and I can free aim but I can't hit them (your version of Phoenix Point), or a character can't completely cover themselves visually, but is in a "cover square" and so I magically can't hit them (XCOM), what's the actual difference?
The aim mechanic seems like a frustrating gimmick at best. You still haven't given a good reason why it should exist, but plenty of reasons why it causes problems and makes everything worse.
So far this game sounds vastly inferior to nuXCOM in every way. Which is surprising given how far XCOM has fallen.
If you want a good alien hunting game, just play UFO: Enemy Unknown. Stop wasting time with all the modern shit. That game didn't even have a proper cover/flanking system and it worked fine.