"It's good design to provide a worse experience to your customers?"
Define "worse". People will complain about doing all sorts of things that are better for their long-term interests.
If you're building a product that provides greater value to users with greater user engagement, then it's in everyone's best interest to promote user engagement, even if that means upsetting the people who would rather gain the benefits of your product without actually using it. You can't make all of the people happy all of the time.