Your theory is correct.
Ideally your sound needs to be processed separately for different locations and uses. The acoustics on stage are likely to be different than out in the house. Also, the type of sound you need to hear for effective monitoring may be a bit different than what works well in the FOH mix.
Unless your cab is full-range and flat-response (FRFR), the sound coming from a Post EQ DI is not very representative of what you hear on stage. Even if your cab is relatively FRFR, it probably will not sound exactly like the PA cabs. So using Post EQ is not really an effective way to deliver the tone profile you envision to the audience.
Most audio techs prefer a Pre EQ DI. Pre gives the audio tech a more neutral starting point, so they don't have to reverse engineer and potentially undue any of the processing you are applying. Pre EQ tends to be way easier for the audio tech to work with. It's sort of like starting with a "blank canvas." If the audio tech understands your tone goals, it's usually fairly easy to massage a Pre EQ DI into the desired ballpark. It's unreasonable to expect the audio tech to capture your tone goals perfect, but they should be able to get fairly close.
An example where Post EQ is preferred is when your amp is actually a significant source of mojo. For example if you have a tube preamp that is pushed in drive territory, it is essential that the DI be taken after the distortion is generated. I generally prefer mic'ing the cab over a Post EQ DI...but many audio techs are reluctant to use a mic on bass as well. If you have a valid reason to use Post DI or a mic, I suggest contacting the audio tech before gig day to discuss your tone concept and try and work things out.
This is not something you should generally work out during setup/sound check because the audio tech will typically be preoccupied with keeping track of and resolving a myriad of little details and emergent problems. So the audio tech may not be able to give you the personal attention you want.