I love it that I can just paste the zip file on foru, here is the file as an addon. When I find the time Ill add buttons for iterations. 
RelaxMeshAddon.zip (6.2 KB)
Here is gumroad link where I’ll be updating it. For me personally its more convenient if the original creator does not mind.
Wow that is really neat. Going to get the addon now. Thanks
Edited: I installed the addon but now don’t know where to find it within Blender 2.8. I hit the N key in edit mode but could not find it anywhere on the side panel under any of the tabs,
Where should I look to activate it?
Thanks
When you enter edit mode it shoud be listed under Stau Tools.
Found it…thanks Staughost. Turns out it doesn’t work well for me. Sends the vertices waaaay off. I will stick with “smoothing vertices” for now.
Could this be done for UVs instead of meshes?
Actually I am working on a thing to make it work on UV-s. To be precise UV>Mesh>Relax>Mesh>UV.
why not UV>Python>UV ?
Well when I understand how to do it in python I will 
bmesh seems to have uv data stored per loop, which seems to be like face corners:
https://docs.blender.org/api/blender2.8/bmesh.types.html?highlight=loops#bmesh.types.BMLoop
and you seem to be able to acess loops from any mesh element.
https://docs.blender.org/api/blender2.8/bmesh.types.html?highlight=loops#bmesh.types.BMVert.link_loops
https://docs.blender.org/api/blender2.8/bmesh.types.html?highlight=loops#bmesh.types.BMFace.loops
If I got it right, there’s no welding, each face contain its own set of loops and they can have any uv coordinate and if two loops belong to adjacent faces and have uv coords that point in the same place, then the uv editor considers them welded and displays one single vert
Whelp I have some reading to do, thanks 