I meant if I was building just a system, it would be obvious to me not to nah that much, or even to provide a means to not be bothered again for 6 months or whatever.

You're right that it's difficult to measure goodwill over long timescales, but IMO not everything needs to be 100% science driven - the team behind Amazon Music must know that excessively, relentlessly nagging already paying customers is going to a not them.

An A/B test should probably measure user complaints. A complaint is an indicator that a user’s usage pattern may change in the future. Of course, it may not.

Although, as a user I’ve learned to complain by canceling (and explaining why when possible).