Sounds good - you are looking for a general solution using the cylinder as a simple example - not that the specific cylinder in question is what needs fixed. It is just representative of a scenario you may need to be able to correct on different geometry. Got it.
Though the Loop Tools add-on might be a better option (I haven’t used it for more than bridging), I think the Relax Add-on under the Mesh menu might also provide a comparable solution. I know that you said “similar distances between all vertexes”, but I’m unsure if the Loop Tools option can work on more than just loops at one time. Also, I know words have meaning, and “similar” doesn’t mean “exactly the same”, so is there a specific margin of acceptable similarity you are aiming for?
See the manual page for the Relax script here: https://docs.blender.org/manual/en/latest/addons/mesh/relax.html#relax