I'm surprised there is a discussion about this with your group.
Everyone pretty much knows... it's a no-no due to safety issues. Plain and simple.
Now, if someone has clip-on aero bars, that's different. They can ride their bike out of areo position and ride it like a regular road bike.
As for TT bikes/tri bikes... with the shifters on the aero bars... those bikes are not allowed on group rides.
I have a roadie and a tri bike. I always take my tri bike out solo. I knew that was the rule when I bought it.
"Life is not a journey to the grave with the intention of arriving safely in a pretty and well preserved body, but rather, to skid in broadside thoroughly used-up, totally worn out, and loudly proclaiming: WOW WHAT A RIDE!!!!"