What Would Have Made More Sense:
Let's go along with the conceit that Xavier won't enter Mystique's mind and force her to step down. None of us are telepathic mutants and we can never fully understand their ways and customs. But ... couldn't he ignore Mystique and just go into the mind of Trask himself, then incept away all his mutant genocide thoughts?
You're already in the comments typing this, but the plot tries to account for it by starting the movie with Xavier's powers being broken. Except they don't stay that way for long. A few minutes after, you know, trying, he's mind-controlling people like crazy. He could have gone right up to Trask, shook his hand, and made him devote his life to, say, breaking the dildo-sitting world record. And to make it harder, he could have scanned the world for the man with the most flexible colon and planted it in his mind as well. It wouldn't have to be exactly that, we guess. The point is he needed something else to do with his life.
20th Century Fox
"Just keep an open mind on this dildo idea; he already has the mustache for it."
It's a movie about saving the world from hate, and they give the main character the one specific superpower that can do that directly. He works hard to make it complicated, but Professor X could do any number of clearly harmless, obviously beneficial things. In fact, once Xavier found out he was going to lose his hair, he could have planted an idea in some TV producer's brain to remake Star Trek, only with a bald Kirk so women in the future would find hairless men sexy. It sounds ridiculou- wait ... dear God ... are we, right now, living in the Days Of Future Past universe?