A physics constraint has around the same performance impact as other constraints. Time will tell, but I doubt it will be a bottleneck. Turning physics movement into keys will require many keys or it will look really bad. A key every 5 frames won't look good. Having many keys has its own performance impact. I don't think baking is a good solution for performance in this particular case.
dodos Although physics are efficient in performance and do not need a key, I think animators should be able to adjust the key as they want.
Note that if physics doesn't give the movement you want, you can key the bones to affect how physics behaves. It may not be easy to achieve looping this way, but it's helpful in many other scenarios.
dodos The opinions I wrote using the translator may not be smooth. Thank you.
Not a problem! You don't have to use English, you can post in any language you like. The forum has a translate button now, so others can translate into their language very easily.