I think it is possible to mix your own sound with a trio, the more members you add the more likely you need a sound man.
We used to use a sound man for our trio when we first got a decent PA but once our drummer mastered the PA and it’s digital settings we sound better than ever.
The getting fully used to all the equipment is an important stage to get through.
I think using the same equipment and knowing it like the back of your hand makes a big difference.
We have gone back to a soundman a couple of times and were not really impressed with the results.
It definitely helps if the drums are electronic too, i think I would always have a soundman with acoustic drums.
Also important is not to have a particularly loud sound on stage so you can get adjustments on the fly.
I think everyone needs to be on the same page for it to work as well, helps stop the fights anyway...