My main argument against BJJ and ground fighting in general (not all BJJ is all ground fighting) is I would never engage in a "jujitsu match" in a barroom or any other similarly crowed area (concert, outdoor festival, etc.). While I was bar tending, I noticed a disturbing trend...
Others would tend to watch and let people fight it out when both people were on their feet. Once it went to the ground, it turned into a free for all with one or the other guy usually getting a foot or bottle to their head.
My theory is people tended to let it be a "fair fight" when both guys were on their feet, and then feel like someone's had enough when it goes to the ground and feel like they have to jump in. I haven't been to those bars in 15 years or so, so maybe things changed since. Maybe that's how it goes where I live and I'm living in some odd bubble. Most likely not to either one of those though.