“Steep” as opposed to “smooth”. For example, looking at the 3D view of your box, there’s almost 90 degree transition from the sides to the bottom of the box. I do see you have a couple polygons there for curvature, but that’s just two polygons for 90 degrees, so on average 45 degrees per polygon. Compare that to the sides that are flipped open - the transition is longer, and smoother thanks to extra polygons for curvature. So, each side (together with the two bottom transition polygons) can be its own island (well, two, for inside and outside surface), and bottom - its own.
Don’t just rely on single-click tools to do everything for you. If you average everything, it’s going to rescale everything. You have some pieces that you say are small and would rarely be seen - don’t include those into averaging. Just pull them aside, position and scale your main shape to give it as much room as possible, then move those smaller pieces back into available spots in the UV space.
Non-quads can indeed be an issue. Quads can be as well, if they’re concave. Both for unwrapping, and for subdivision/sculpting etc.
The thing is, if you’re considering sculpting, there’s a good chance that you wouldn’t want to use your low poly as base, at least not as is. For sculpting, ideally, you should use even square quads. Anything else would lend to stretched detail.