Is there a reason why some types of railcard (e.g. 16-25) have photos but others don't?
Some thoughts.
Seniors are seen as relatively unlikely to break rules while young people and particularly students who have recently left home are seen as relatively likely to do so.
The Family railcard legitimately allows travel with either parent (technically either cardholder), and multi-family households are unusual. The abuse potential seems relatively low.
Requiring photos from disabled people would open up a huge can of worms. Some disabilies are associated with disfigurement and others would make it difficult to use a photobooth.
Two-together by it's nature would be especially prone to abuse if it didn't have photos, it's also a relatively recent creation.
I do find it somewat surprising that the network railcard doesn't require a photo, perhaps it relates to the fact it wasn't originally a photo at all.