Should PMs (AI) code?

This is a matter that is close to my heart as I was a PM for about 7 years before switching back to development.

First, there are two sides to this:

• Coding prototypes. This used to be a skill that some skilled and technical PMs were able to perform relatively comfortably in order to generate artifacts of high fidelity (fidelity to the medium and the feeling the feature needs to convey rather than to the actual design of the feature), which is now even easier to perform.
• Pushing code to production. That's the other end of this spectrum, where a PM is functioning close to the development team and, on top of doing their regular PM tasks, they also unblock the team by taking smaller tasks that don't fit in the sprint's main goal.

I've heard a lot of voices stating that the first option is the best one and I would agree, if I was to take the PM's mental health into consideration. Doing both is a lot and can be taxing for the individual, but I've also worked with some amazing folks who have somehow been comfortable doing both. As an engineer I tend to appreciate the fact that I have less distractions during the sprint but stuff still gets done.

What are your experiences both as PMs and engineers? What has worked well for you and what has not?