In the end if there is no compete clause in your contract, you can just not take it...
Though, I wouldn't mind keeping my own "non-termination agreement" on hand so that if I am asked to sign a non-compete, I can ask them to sign my contract too.
After all, if they think it's fair that I shouldn't be able to work for another company doing the same thing, it should be equally fair that they can't replace me with another worker doing the same thing.
So yeah, I'll sign your non-compete, so long as you agree that you cannot terminate me without invalidating it.