I'm not a host, but a guest. I came to this thread because I discovered that hosts are allowed to refuse or even cancel a booking for someone without a profile photo and was really shocked to know that was permissible.
My wife and I are in our 70s and have been using AirBnb a lot over the past few years. I like the notion of making a personal connection with the owner and, in fact, I tend to use apartments where the owner self-manages whenever possible. I have a profile and it includes a photo... but...
I can't actually think of any valid reason a host would need to see a photo other than some sort of discrimination. Some folks on this thread think there are valid reasons, such as being able to tell whether somebody is a suspicious character. I'm a little dubious about such a claim. I think it usually means the person doesn't look like oneself in some way or another.
But discrimination is not the only reason that people don't post photos. Plenty of women are trying to stay hidden from abusive ex-spouses or boyfriends. It seems entirely proper that such a person may not post a photo.
It seems to me that anyone using AirBnb should be free to post as little or as much about themselves as they like. If the absence of some info (photo, life story, etc.) causes you to reject the booking, then so be it. At least then nobody can accuse you (for example) of discrimination because you saw the picture and then cancelled.
It's also worth noting that AirBnb is an international company. It can be sued in lots of different national jurisdictions under different laws. It seems quite natural that they would not want to be the ones to filter out your unwanted guests for you. The legal side of it would just be too complicated.
One last thing... if AirBnb wants to know the names of all my guests, then they have to stop sending advertising to everyone whose info I enter. I initially used to list my wife, who has a different last name. But after she was dunned with solicitations to sign up for AirBnb herself, I stopped responding to the part that asks for the names of guests. I simply tell the host that I'm coming with my wife and nobody has ever batted an eye at that.
Finally, there is that: AirBnb asks you to write to the host when you attempt to book. Plus there is the profile. If you don't like what you see, then don't accept the booking.
My two cents as an unaffected but interested member. YMMV.