Hi Leslie,
Just remember that if the person who stays at your place damages anything and turns out they aren't the holder of the credit card that paid AirBNB, you cannot hold the payer responsible since the payer didn't cause the damage. That's the only reason to care about people without a profile picture. At least with the profile pic you can make sure the person who booked is the person who would be held responsible.
You also leave yourself open to host-jacking. Which is where a 3rd party books your house without a profile pic, then re-posts it on another platform, and makes a profit. Again, if the person renting from the 3rd party were to damage your house, they could not be held liable - you wouldn't even have their information.
Best,
Laura