> However at the end of the day he's working with Gaussian noise assumptions, just like everyone else, and the solution is obtained by some form of Least Squares, again, like everyone else.

Well you need some kind of model to optimize, and finding the perfect one is a vastly more difficult problem that probably begins to incorporate some stuff from information theory (which starts to become rather a different field).

I don't actually see the issue with researchers working on algorithms to solve the Gaussian noise versions of these problems — they can usually be extended to some other model relatively easily (for instance, rotation synchronization via Riemannian manifolds can incorporate a Pseudo-Huber loss function without much difficulty).

Also, what is SOTA?