So I've seen this handled a few ways by companies that did allow it.

The companion fights with you but doesn't take up a party slot. This ended up being bad as the companions had poor ai to keep the processor time down for the ai. Standard practice was to disable the companion when starting a dungeon because the poor ai would constantly screw up positioning and pulls. This doesn't even get into the issue of people using tank companions that would taunt aggro off the real tank so that the boss would turn and cleave the entire party.

The companion fights with you and takes up a party slot. This meant less companions and they had a somewhat better ai. There were still cases of them going braindead and causing problems however. The big issue with this would be that in a trinity system a tank and healer could easily pull out dps companions and micromanage them and never need a dps to run a dungeon again. DPS queue time would skyrocket, and there would be massive balance issues because of that.

This doesn't even get into the whole multiplayer game aspect, where part of the design of dungeons is that you should be doing them with other people. While having your companion be more useful would be great, I just don't see it happening, I think SE got this part right as it pertains to game design and balance.