Using the word precommitment makes it easier to talk about these things (unless you find yourself in an argument like this) and finding a reason to treat just this one case as an exception can genuinely be in the best interest of a particular instance of you that already finds itself in that exception (this is more obvious with time travel scenarios than with game theoretic scenarios), even though overall eliminating such exceptions is in your interest (since it will reduce the probability of the circumstances of these would be exceptions arising in the first place).
Using the word precommitment makes it easier to talk about these things (unless you find yourself in an argument like this) and finding a reason to treat just this one case as an exception can genuinely be in the best interest of a particular instance of you that already finds itself in that exception (this is more obvious with time travel scenarios than with game theoretic scenarios), even though overall eliminating such exceptions is in your interest (since it will reduce the probability of the circumstances of these would be exceptions arising in the first place).