Yes. I have never not micromanaged workers. You know that AI that's super easy to beat and a lot of people can beat on Deity? Ask yourself if that's who you want running your workers. Pretty straightforward answer imo. But, yaknow. I also kind of enjoy doing it. So even if I was not much better at knowing what is good for my Civ than the AI, I'd still do it. There's also synergies, i.e. chopping down forests, that the AI can't possibly comprehend as it is ONLY dealing with your tiles while you're running the entire civ, building buildings, constructing wonders, and potentially waging war. I can vastly improve my chances of getting an early wonder by chopping down a couple of forests, for example.
If you have a time crunch on multiplayer, then yes, sacrifice workers and have the AI run it. Because it is certainly the least important thing for you to devote attention to given that you CAN have the AI do a REASONABLE job of it in your stead.