Forcing an electric bassist to go DI is like close-micing a concert violinist and disregarding the reverberation of the concert hall, which is really part of the instrument.
I've gone the same route as BurningSkies. My amp is still part of my sound, but my speaker cabinet is not. I give FOH a post-eq DI, and so far it has worked for everyone. Sometimes, the sound person says something like "can you take down 200 Hz a bit, it's booming in the house?" and I immediately comply. Does FOH sound just like my amp? The recordings seem to indicate it's pretty close. Anyway, it's a way for me to give them the signal I want, and for them to minimize their effort. So we each get what we want, without fussing or fighting.