I agree with you in theory

If it were a one-time purchase, wouldn't that encourage the service provider to make it worse over time because they've already taken your money?

Couldn't it encourage the provider to make it better because their revenue comes from new customers?

if the service gets worse, simply cancel your subscription.

There's plenty of examples of subscriptions that are nearly impossible to cancel, or have a giant fee for cancelling early. Adobe, Comcast, siriusxm spring to mind. Anecdotally, streaming services are partly funded by people who subscribe for a particular film/tv show and just never cancel.