No, that doesn't make sense at all. You've paid for consistent terms for that Y period of time. Not cancelling the subscription when it's up for renewal is an implicit agreement to any new terms. And I'm sure if you'd read those terms in the first place, you'd come to the same understanding.

(And it's not even that: the X you're charged is subject to change upon renewal!)

I'm not arguing that this is a good or bad thing, just pointing out the reality of every single subscription agreement I've signed up for online.