OP, these forums are not the best place to get this question answered. As has been repeatedly demonstrated over the last 20+ years, the official forums of any game are where the zealous die-hards gather. They are not a representative sample of the population of the game as a whole, asking this group won't give you the real picture.
To answer your question, there have been many polls on this subject in other locations, and the consensus seems to be, about 80% of the players play in Solo or in Private Group mode, and the overwhelming reason given for that is the desire to avoid nonconsensual PvP.
So, yes. I strongly suspect if they did away with the Private Group option and instead had two login options for Open, those being PvP Enabled or PvP Disabled, you'd quickly see a lot of people moving over from Solo.