There is a philosophical assumption underpining astronomy and cosmology, the so-called "cosmological principle."[0] This is an assumption (albeit not completely unfalsifiable) that physics across the universe at large scales is the same for all observers, that here on earth there should be similar to physics in andromeda.
Of course, all scientific experiments done have been done on or near earth, and thus, our interpretation of astronomy on earth is tempered by experiments we do here, for example, we assume that the speed of light here is the same as the speed of light elsewhere.
This is, in principle, a problem. We unfortunately have no way to measure the speed of light in andromeda, unlike what we can here on earth, so we really have no idea if our astronomical models are wrong given the non-constancy of the speed of light in andromeda or elsewhere.
So, yes, in principle not being able to repeat science experiments everywhere in the universe is a problem. However, I think if one thinks a little less broadly, testing newtonian gravity in say, Italy and also in China shows at least across the Earth, the phenomenon is similar. Then, at least one can say, "certainly, gravity is the same in Italy and China, and perhaps across the surface of the Earth." That is a stronger statement than "gravity is this way in Italy." Ordering claims by "scientific goodness", we can say that
Gravity is the same *across the universe* > gravity is the same across the Earth
> gravity is in Italy
My point here is that even if one can't fulfill the extreme of testing theories everywhere in the universe, one can progressively prove stronger and stronger statements regarding the validity of scientific theories.
Somewhere the LHC stands between "the SM is validated across the universe" and "the SM is validated at one detector at the LHC". Yes, it would be "better" if the Higgs was found at other experiments, but the current situation is "better" than if the Higgs was found at one detector there and not in any other. Repeatability, like everything in science, is not a binary step function but is some continuous function over the domain [0,1].
[0] https://en.wikipedia.org/wiki/Cosmological_principle