see having rider means he can go out of his way to break said contract
Yes, perhaps, but not in a way that would harm Rin. He can't be sure Rider will remain loyal to her, for one thing, and he
certainly wouldn't trust Kotomine.
Also, to some extent that can be a plot point. Have at least some aspect of Archer breaking his contract with Rin, and then have Kotomine try to take Rider, only for Sakura to take her back at the opportune moment.