It's basically the opposite situation from 150 years ago. Back then, we thought our theory was more or less complete while having experimental data which disproved it (Michelson-Morley experiment, Mercury perihelion, I am sure there are others). Right now, we know our theories are incomplete (since GR and QFT are incompatible) while having no experimental data which contradicts them.
Doesn't that imply our theories are "good enough" for all practical purposes? If they're impossible to empirically disprove?
The point being it's not at all clear what we might be missing without these impractical little mysteries that so far are very distant from every day life.