I tend to think people go camping to get away from people...not to judge them. I certainly don't think there is an unwritten rule that you have to have a dinky tent if you are by yourself. If you were to rent a cabin just down the road from the campground it would be bigger than your 6-person tent. I have a 6-person tent that I can walk into (7'6" at the peak) that I use car camping with my family. It is nice! but not a deal breaker. I certainly wouldn't buy a different tent if I had a free one I couldn't walk into available.

Backpackers who want to be able to stand up buy a teepee style tent. Pretty simple design, but to get it in a weight suitable for backpacking they have an awful lot of expensive lightweight fabric. When I was looking for a backpacking tent for my family they were too expensive for me. Plus you only get the head room at the peak with very steep walls. I am not sure how beneficial that is.