I have generally not been satisfied with attempts to EQ the high frequencies even on modest priced speakers. However, I recently started using FIR filtering with a tailored inverted impulse response from my room's measurement. The tailoring of the impulse involves only EQing things that can be effectively addressed by the processing, so it leaves high frequencies basically untouched. If the filter is somehow ruining the high frequencies it's not processing, I'm not perceiving the loss. I like running it all together to keep it all time synchronized. The FIR filtering introduces some latency.
Nevertheless, now that you've mentioned it, I am running an active crossover and can set the FIR filter to only work on the bass channels, and I can delay the highs as needed, so I guess I'll give that a try.
I should add that I have used EQ on tweeter/horn lens combinations of my own assembling, and they really do need the EQ. Getting it right is a long process involving a lot of measuring and listening until you get some idea of what measurements correspond to what perceptions. Shooting for perfectly flat on axis never seemed to work.