People tend to look worse in video chat than they do in real life.
I'd be careful of any girl attempting to push this as there's a good chance she's looking for flaws. She can scrutinize you without having to deal with any in-person charisma and kino-ing getting in the way of her agenda/process.
Another angle is that she may want you to "see her at her worst" because otherwise how are you going to deserve her "best"?
Kind of like how women will push for a phone call and then mumble their way through the entire phone conversation. Or wanting a "right now" pic while you are texting her late at night and you are likely both tired and haggard. So they can scrutinize you while
lowering their perceived attractiveness at the same time.
As
@Modern Man Advice said, "they want to play it safe and get a feel for you before making any effort." I wouldn't have a mindset of simply complying though. As with any kind of game or war, you need to strategize against an opponent.
I'd only engage in a video call if the female was at or near the top end of your range, and be careful to makes sure your presentation is on point. But first I'd try and screen out these kind of women. They're basically announcing they require more work for you to get laid than the women who don't demand a video call. If there's a bunch of verbiage in their bio/profile about "God" or "No Hookups" or "Looking for my soulmate" there's a good chance they will want a video call (if they don't state it directly)
Another option is to build up more comfort/attraction before asking her out for drinks. If that doesn't work, say you have a headache, minor family emergency, or a super-busy schedule if she tries to schedule it for a different day. If she still insists and you aren't that into her, I'd just let her go (unless you want to practice your video call "game").
And as a final point, video calls can hide fat as well as any Myspace Angle.