My take is the modeling is sort of like back seat driving. You program your modeler to sound good with a certain amp, in a certain room, at a certain volume. As soon as one of the parameters is changed, the model is no longer optimized and the audio tech has to be free to make some corrections.
Also, chances are you will setup and tweak the modeler while playing by yourself, so you don't really know how well it will work in a mix.
I am not saying modeling is not useful, I am saying the idea of sending a signal to the audio tech with idea that it is perfect and should not be tweaked to the needs of the mix in the specific acoustic environment of the gig is unrealistic.
As an example, I used to run a digital board. The setup at the end of the show served as the starting point for our next sound check. One might assume that I could simply adjust the trimmers on the channels to rebalance levels and that is all that would necessary, and on some occasions you would be correct.
But on other occasions, a massive amount of changes are required to system EQ, individual channel EQ, compression parameters, effects levels, etc., to dial the mix in. I tended to save the ending state of the board as a recallable scene. These scenes were most useful when switching between indoor and outdoor gigs. I tended to keep an indoor scene and an outdoor scene. It might have been useful to keep a wider variety of indoor setups but I never really put much thought into how to grade and classify different rooms.