Literally animating sounds like a lot of effort that can't be reused. But it has occurred to me before that it would be reasonably easy and quite entertaining to make many of the solvers able to output a save file, which you could then load back in to the ordinary GUI and hit Redo repeatedly to replay it.

It wouldn't show you the whole story, though – some of the deductions the solver uses have no direct representation in the visible UI. For Net in particular, most of the working state of the solver has that property: there's no UI for storing even the set of not-ruled-out orientations of a tile, let alone the state of an individual edge or the max-reachable-squares counters. So it would only be pretty – it wouldn't be especially useful as a debugging aid when the solver had a bug, or as an insight into what the solver had spotted that you hadn't if you were trying to use it to debug your own thought processes.