Consent is important whether or not someone is physically with you or watching you over camera. You can force someone to masturbate, or take advantage of their inebriated state to make them do what you want them to. Just in the way that some members try to blackmail models into doing what they want. They are not physically touching them, but they are gaining sexual reward by using force.
It is a very difficult road to navigate on whether anyone would be to blame in this situation, because a member could be indirectly taking advantage of the models current physical condition which causes her to not be fully in control of her decisions. The member might not be aware of this. Not dissimilar to if a prostitute were being trafficked and forced to see clients by a pimp, but the clients were unaware of this. The prostitute is being raped/forced to consent, but where does that leave the client who has taken advantage of the situation?
Bringing alcohol and excessive inebriation into the mix complicates matters and I can see why camsites would not want consent to ever be questioned. It's a matter with so much grey in it that it is impossible to navigate. The cam model chooses to drink alcohol and put themselves in that position by getting on cam, but then there are certain acts that a model would not ordinarily perform.
I came on cam with two of my friends years ago while we were drinking at my place. Neither of them had ever cammed and wanted to see what it was like. One thing led to another and people kept tipping us. We didn't really do much, though one of my friends got very excited and at one point said "X amount of tokens and I'll dildo myself!", to which I put my foot down (much to the disappointment of the members). She was very drunk, she was getting excited by the attention and the tokens. But I know that she did not want to do that, and she never would have said that had she not been drinking. She came to her senses after I said no and thanked me, but the guys in the room were still trying to pressure her into it and started tipping for it. I could have seen how had she not been with me that they could have taken advantage of that and forced her into doing it.
It is easy to say "but they aren't in the same room!" as an excuse to say that the person behind the camera couldn't be forced. But peer pressure when you're on screen can be pretty intense, especially if you aren't used to it. Let alone if you weren't in a consenting adults frame of mind.
So yes, I imagine it is largely due to consent and the sites making sure they cannot be held liable. I could see there is also the possibility, due to the nature of the work, that they don't want to be accused of encouraging girls to drink. If girls are encouraged to be intoxicated on camera then there are likely a whole load of things to worry about, addiction, death, consent etc. So by having a flat ban you basically eliminate that risk.