Quantum mechanics, special relativity, and general relativity (I'm not sure which ones you're objecting to here) all have strong predictive power. The fact that we can build extensions of these theories and see experimental validation of those theories is itself support for the underlying principles. With quantum mechanics, you can explain atomic spectra, crystal field splitting, aromaticity and antiaromaticity, vagaries of chemical bonding--and that's only in the domain of chemistry. Special relativity can also explain, say, why there is a stable Pb²⁺ ion.
I know that's a terrible analogy, but proving GR kinda works doesn't really disprove the Ether, either.
Quantum mechanics is an ur-example. Fundamentally, it's a set of mathematical equations only some of which have clear physical interpretations. What does the wavefunction actually represent, for example? To make matters worse, it also relies on mathematics that are well outside the comfort zone of most lay people--complex probabilities and renormalizable groups, for example (the latter caused consternation even within the physics community before the underlying mathematical basis was more rigorously developed). That leads popular description to rely on analogy that is at times more obfuscatory than helpful. But the underlying mathematics is quite well-understood, and we've built successful validations across chemistry, physics, and biology. As Feynman said, it's the most well-validated theory in history.
If you want to get a new scientific theory established, you need to do one of two things. The more common scenario is that you explain something that wasn't explainable beforehand. This is basically what quantum mechanics did. The less common scenario is that you find a much simpler but equally powerful explanation--this is what special relativity was.
The point of the Michelson-Morely experiment was to find the Earth's motion relative to the inherent reference frame of the universe (the ether). With the discovery of Lorentz invariance, Einstein's relativity theory basically said "it doesn't matter, any reference frame will do." Given also the many wavelength-dependent properties of light meant that you couldn't reuse the wave equations to explain electrodynamics, there was no reason to keep the ether around. Sure, you can build theories on the ether, but you're not getting anything simpler or more accurate by doing so, so what's the point?
The implications are phenomenal, -- we could be in the presence of something HUGE, -- but people seem to rather "know for a fact" that we live in an empty vacuum devoid of anything but relics of a big bang.
I dispute that premise; it seems to me unlikely that we know anything from certain, and it seems to be that expanding our understanding of the world has had diminishing returns; fire has had greater returns than agriculture, and that engineering, than Newtonian mechanics, that than relativity and quantum mechanics, and so on.
From the above observation of the utility of scientific discoveries, if Ether theory nevertheless is closer to how the world functions, it seems very unlikely, and the conditions that enable it to exhibit its characteristics seem so alien to our present way of life that it is unlikely that funding research in such a direction gives better expected returns than research into other questions.