The counterpoint is that if we were more eager to ditch theories as soon as they fail to explain absolutely everything in the universe, we'd have tossed Newton's laws in the early 1800s because they didn't accurately predict the orbit of Uranus.

(turned out they did, but nobody at the time knew to account for perturbations caused by the as-yet-undiscovered Neptune)

And depending on how far you want to take this, the neutrino probably would've been dismissed, too, before eventually being detected.