But like you said, you also run the risk of flipping the car. It would be interesting to see some actual data on this. It's the sort of thing that has been repeated so much that it's easy to make bad assumptions.
Anecdotally, I've almost hit a moose two times. Both times I just completely froze up and slammed the breaks. They jumped out of nowhere, the only reason I didn't hit any of them was just pure luck and timing, and had nothing to do with my ability to react or steer away.
The latter circumstance feels extremely unlikely considering SUVs are generally engineered to support the higher likelihood of more weight ending up on the roof of the car in the event of a roll-over. I'd be surprised if SUVs had weaker structural reinforcement than equivalent-classed sedans.
But I could be very, very wrong here and wouldn't be surprised if I am.
Any data on this? Bigger==safer doesn't always hold with these things. Lots of other car design features play a role there, e.g. a smaller car with a strong roof will likely beat a SUV with a weak roof structure.
(and while lots has happened with safety technology, the classic counter point is that if you have a chance to avoid the crash you're way more likely to roll an SUV while attempting to do so)