It's worse than that. If you don't own the encryption keys, it's not your computer anymore.
Not only will your software expire if you don't pay the rent, all of your documents will be locked up too.
You might have a built-in rootkit that's exploitable by whomever wrote the software.
It would be a marketer's dream come true. Imagine logos, pop-ups, banners all over your screen and you can't turn them off... unless, perhaps, you pay an extra fee.... maybe.