If you never actually took the steps to cancel your contract won't they be able to prove your debt via the existence of a non-cancelled contract?

The purpose is to take advantage of the sloppiness of the debt collection industry. They are designed around tricking financially illiterate people, harassing poor people, and lying.

When they buy a debt, they rarely get comprehensive documentation.

you will end up with damaged credit. The only negative on my credit report is from a verizon phone I bought from a verizon store (actually ended up not being Verizon owned store,) which i returned within the 7 days return fee, even paid re-stocking fee. But which the store credits me for having returned it later than I did, which allowed Verizon charged me 1 month service fee, which I never got a bill or email even though verizon had both, until it showed up on credit as collection. Nothing I did could get it off.