A spinning bar will be much harder to grip, this is why you will often see tourist scams that say "Hang 100 seconds for 100$" and will cost 5$ to attempt. Normally hanging for 100 seconds is fairly trivial for someone who is in shape. Rotating bars make it impossible to use false grip or regrip while also making it significantly harder to just hang on.
(Pro tip for those scams: Sometimes they don't specify which grip you can use. If this is the case, use an alternate grip. One underhand and one overhand, it will counter the spin to make it significantly easier.)
- It will increase your grip strength.
- It will be significantly harder to work other muscles properly.
- Strict muscle-ups will be near impossible because you can't false grip on spinning bars.
From past experience I would not recommend building a bar that spins unless you are looking to train for the hanging challenges. I ended up building one with a bar that was too thick, which also makes it much harder to grip, and regretted it every time I used it. If you do build one with spin, make it possible for it to swap between spinning and fixed, so it serves the best of both worlds. A simple hole drilled through the bar with a removable pin in it will work just fine.