The scan specifically says their willpower WASN'T enough to stop her power from working.
My bad, I worded it wrongly, I meant to say that his willpower will be enough to stave off the effect of her hax long enough to reach for the ID core.
You could take the implication, but what it says is that their willpower wasn't enough for the strongest and most visceral emotions being shoved into their mind by force constantly. Strong Master powers in general really don't care about the will of the target, Worm just kinda isn't that setting (the closest guy to supernatural will I can think of is Chevalier, who almost had their cape name be "relentless" instead and walked out of a hospital freshly after having his abdomen stapled back together just to fight an invincible Kaiju that could kill him by pointing)
Supernatural Willpower doesn't automatically give any resistance to Empathic Manipulation unless there are feats of that specifically. His willpower may be strong, but these are the strongest emotions he'll have felt in his entire life; these emotions are strong enough to make highly-trained ex-military soldiers kill themselves in a matter of seconds
Wildbow (Parahumans author) has stated that even if you're specifically trained and highly experienced against these powers, it is only possible to semi-effectively delay the onset; for someone with no experience against this kind of thing and no idea what's going on, the chances aren't great regardless of willpower.
While it doesn't automatically cover that in a straightforward manner, Ace is a completely different beast than anyone you have mentioned here. As I've said, Ace has gone through over 2000 years competing and winning in death games and battle royales to find his mother across different reincarnations. At any point (especially in such a long and arduous length of time) he could've just said "**** this," and give up on his desire, but he pressed onwards till now. Hell, his willpower is supernatural in the fact that it allowed him to not only reincarnate many times within those 2 millennia, but transcend it and still retain his memories. Not to mention,
to keep his mum alive,
Geats literally willed a new rider form into existence. Geats' willpower completely and utterly tops anything the Parahumans series considers supernatural willpower by kilometres, even those with training. There's no way he won't be able to power through, and it just gives him some trouble at worst.
Personality and raw emotions are different, much less memory being a totally different power to manipulate. Not entirely sure how much it would apply in this case
Memories, personality, and desires are completely separate things from emotions. A change in emotional state after a change in one or more these things makes perfect sense because of how strong an influence these things have on emotions; however, this does not automatically mean it also grants resistance to emotional manipulation in the absence of further evidence
Desires bring drive to a person. Their personality, memories and emotions are determined by their desires, especially if it is dear to them or a matter of life or death for them. They'll do whatever it takes to pursue and eventually make their wishes come true (like Keiwa donating for his desire for world peace and Neon running away from home). Take their desires away, and you're basically ripping away what they are and what they have become. Now Keiwa always feels lazy and unmotivated and Neon, who originally has much disdain for her family, is now enjoying the fixed arrangements her family had made for her. All of that stays permanent till they touch an ID Core (anyone's one is fine, it works the same).
TLDR: It isn't just the emotions that are being manipulated, desires come in packages of it among other things. And the ID Cores cover this up.
Cherish can force him to feel doubt and apathy to prevent him from doing that
An action that is just reaching for the middle of his belt will just be easy pickings for his willpower. And from the scans I've read, the manipulated emotions feel disconnected rather than being derived from the receivers' personal baggages and whatnot. Sure, she has the telepathy to see to it, but her reading seems vague (case in point being that she'll just know that Geats is fighting for his desire to find his mum. It's not like the memories or thoughts would be warped to fit the manipulated emotions. Straightforward emotions based on what Cherish gets from her telepathy can only go so far without being able to completely tap into Geats as a whole.
If he's able to figure out that her power is manipulating emotions before he gets enough depression to commit death then sure, but unless he's had experience with emotion manipulators in the past, I feel like his first thought upon feeling crippling depression, apathy, and self-loathing probably wouldn't be that his emotions were being manipulated, it'd probably be depressing, apathetic, and self-loathing thoughts, especially if he had no idea there was an emotion manipulator in play at all
I think this is just countered by what Geats as a person is. Ace is the kind of guy that always knows what he's doing (no matter how outlandish it may be), planning steps ahead to get closer and closer to his one desire to find his mum. The moment he starts to uncharacteristically falter, or any foreign emotions start to plague him, he's going to sense something amiss about his opponent. In the event that he somehow gets his emotional buttons pushed in the wrong way, it's going to be more detrimental to Cherish rather than Geats because he'd just rage, and either
go all out or
will a new rider form to deal with Cherish no holds barred.
