What motivated Einstein's work (and that of other, less successful theoretical physicists at the time) was the mathematical impossibility of classical mechanics and classical electrodynamics both being correct at the same time. After all, his paper that introduced special relativity was called "on the electrodynamics of moving bodies." There were no mirrors involved.
In other words, the Standard Model isn't even consistent above a TeV or so without the Higgs. Something has to give.
Edit: to make contact with your example, everyone knew that if you didn't find evidence for the ether, than the model of electromagnetism was very wrong. In fact, that was great justification for carrying out Michelson-Morely type experiments.
That assertion doesn't make sense as you invoke Einstein to support it. Einstein was a theoretical physicist. A more accurate and less sensationalistic assertion could have been : one theoretical model > another theoretical model.
In modern particle physics the main limitation is lack of experimental data. To get that data we have to build giant and expensive experiments like the LHC. Even if the LHC is completely successful we're still going to need bigger colliders to test other things at even higher energies.
Another problem is that the current theories make predictions about things that we probably won't ever be able to measure directly due to the microscopic scales involved.
To name an example. We think that gluons exist inside atomic nuclei, but we can't observe them unless we break the nuclei apart, thus destroying the gluon's habitat. We think it's there because we see what looks like the energy of a gluon falling apart, and because mathematical models back it up.
I presume you're using quotes around "failure" to remind us that, in fact, there has been no such thing.
We haven't explored the full energy range where our models suggest the Higgs boson(s) could live, and even where we have searched, we haven't accrued enough data for a statistically significant result--positive or negative.
Claiming we have failed to find the Higgs is like claiming tigers don't exist without leaving New York.
Of course, they may find the Higg's boson tomorrow, and then my little theory about them being wrong would be proved wrong, but that's science for you.