Occam's razor is perfectly empirical: "entities must not be multiplied beyond necessity". It's what people repeatedly accuse string theory of violating in low-rent popsci criticism.

The other things you refer to are still Occam's razor: symmetry is handy because it eliminates symmetry-breaking entities even though we know they can happen in the standard model (Higgs) and "beauty" is really just another way of saying Occam's razor - you'd prefer your theory to not be full of dozens of free parameters because it starts to fit any possible outputs and be less predictive.

At all points the issue is that unless you've fully explored a simpler space with less entities, don't start adding them because you can always keep adding them to solve any problem but predict nothing (ala epicycles keeping geocentric solar models alive. You could probably run a space program assuming the Earth is the center of the universe, but it would be fiendishly difficult to model).