You have to do estimates, it's how a business works. Not knowing when something will be delivered is too much to ask a company to deal with.

Also, "always do the simplest thing" is one of those phrases that can be twisted and morphed to support literally anything, which makes the phrase useless. It feels good to hear and say, but the reality is it doesn't help you out of a jam.

Sprints are exactly what you're describing, except with accountability built in. That shouldn't scare people, but it does, and that is what causes burnout. Fixing the fear around accountability is how you fix burnout, not eliminating the thing that your boss can use to justify your job.