Is there any way to Bake a texture from world-space to uv coordinates

So lets say I have a mesh. It has UV Coordinates, but those coordinates are smooshed and not all that useful for, say, slapping a circle/square/line texture on it. But I need the coordinates to stay that way for other purposes.
What I can do is: just run that texture through a world-position node instead of the coordinates, and bob’s your uncle.
But what if I then want to bake that texture out?
Effectively, I want the texture to be baked on to the uv coordinates in the same smooshed manner as those coordinates.
Is there any way to do this?

Even if you baked out that texture, it’s still just a texture being applied to a mesh, and that texture is going to be applied via your messed up UVs. Why not add another (proper) UV set and use those for the texture you need to not be “smooshed”?