In last scene of the movie X-Men: First Class, when Sebastian Shaw was 'paused', and Magneto wore Shaw's helmet, Xavier did nothing but cry! Instead, he could have used Sebastian to take the helmet from Magneto and destroy it. At the very least, he could have saved Sebastian's life. As Sebastian was much more powerful than Magneto, Xavier's success would be 100% guaranteed. But Xavier did nothing. Why?
By this point X and Magneto had become close friends. Even long after this point in the comics Professor X was still trying to get Eric back on the path of believing humans and mutants can be friends.
He possibly could have tried to use Shaw, but that would have been a great risk. Shaw was an extremely powerful mutant and it would have been difficult to control him to the degree required in order to have him merely disable Magento and not kill him. Professor X probably saw that as too great a risk to take with his friend.
Two things occur to me.
Xavier was still friends with Eric and things hadn't escalated to open confrontation between them yet.
Shaw was also more powerful than Xavier, and perhaps freezing him was as far as his powers could go. If he'd unfrozen him, Shaw could have still destroyed Magneto. Maybe. He was still loaded with nuclear power.
Because it would break his "golden rule" of controlling people. He freezes or manipulates or plants suggestion but rarely if ever takes control of a person and removes their free will. It's like Batman's no kill rule... Xavier doesn't like entering heads unless it's necessary and even then will only go so far. Arguably he did it once and once only, to his parents to make them take in Raven/raise her as a sister.
Controlling Shaw as a weapon would be taking the dark path to him... so he tries to reason. Even Raven tells him he can "stop her" going with with Erik, but he won't... even at the point of her killing Trask in DOFP he does not prevent her but tries to reason. He knows of all the mutants and their powers the one that would be most feared among humans is the power to take their free will from them. Once he does it, the genie is out the bottle.
Since Shaw had the power of absorption and subsequent redirection of kinetic energy, how would any earthly imprisonment work unless suspended in thin air the whole time because if not, he'l just run into a wall or fist himself a hundred times until he'd redirect his own blows to break through solid rock and what not and obviously it wasn't an option for professor X to permanently render Shaw a vegetable since it would permanently tax his mutant power........ Hence, he was too dangerous to be left alive and thus had to die!!!
Shaw's execution came after Prof. Xavier found that Magneto and Shaw were unreadable in the reactor chamber. Xavier was unable to affect the events, and was anguished by the knowledge of Eric's intent. Charles Xavier was a witness, not an effectual participant. He could control neither of them.