I wouldn't say that we have no experimental data which contradicts them. Rather, we do have experimental data which contradicts them, but no experimental data that points us in the direction of a solution (and whenever we go looking for the latter, we fail).

Consider e.g. neutrino masses. We have plenty of experimental data indicating that neutrinos oscillate and therefore have mass. This poses a problem for the standard model (because there are problems unless the mass comes from the Higgs mechanism, but in the standard model neutrinos can't participate in the Higgs mechanism due to always being left-handed). But whenever we do experiments to attempt to verify one of the ways of fixing this problem -- are there separate right-handed neutrinos we didn't know about, or maybe instead the right-handed neutrinos were just antineutrinos all along? -- we turn up nothing.

I disagree, but maybe only because we are using different definitions. For example, we have neutrino oscillations, this requires neutrino mass, which is not part of the standard model of particle physics. In cosmology, there is "lithium problem" (amongst others), which cannot be explained by Lambda-CDM. We know our physical theories are incomplete not only because our mathematical frameworks (GR & QFT) are incompatible (similar to the incompatibility of Maxwell's equations and the Galilean transformations that form the basis of Newtonian mechanics), but also there are these unexplained phenomena, much like the blackbody radiation at the turn of previous century.

>GR and QFT are incompatible

I did physics at uni and kind of dropped out when it got too hard.

I've long guessed the incompatibility is because the maths is just too hard for human brains, though I'm probably biased there, and we'll get a breakthrough when AI can handle much more complex maths than us. Probably not so long till we find out on that one.

I once tried to write a simplified explanation for why a spin-2 quantum theory naturally results in something like general relativity and totally failed - man that stuff's hard.

What about underexplained cosmological epicycles like dark matter (in explaining long-standing divergences of gravitational theory from observation), or the Hubble tension?

Doesn't that imply our theories are "good enough" for all practical purposes? If they're impossible to empirically disprove?

This era might be one where we have to earn the next clue much more slowly

I find the idea that reality might be quantized fascinating, so that all information that exists could be stored in a storage medium big enough.

It's also kind of interesting how causality allegedly has a speed limit and it's rather slow all things considered.

Anyway, in 150 years we absolutely came a long way, we'll figure it that out eventually, but as always, figuring it out might lead even bigger questions and mysteries...