It's a tradeoff that seems to be working in the balance at the moment. If someone captures all your snaps currently, you know, maybe you can disinterest him. A ban on screenshots takes that knowledge from you and pushes it off into the realm of video screencappers. There you have no idea who is up to what and the incentive to limit how many snaps they save goes away if they go to a method where it doesn't report back if they're naughty or nice.
Which would be dead easy to automate and no I'm not sharing a how to. It's kind of like recording songs off the radio back in the day. (These were tape days) Record companies didn't like it, but it wasn't a big thing and it let fans enjoy their favorite artists. Later came digital piracy which didn't even require being by the radio to hit record on the tape player, and Napster fan though I was since it was an amazing music discovery vehicle, that was a broken model from go. In the end the record companies had to change their model entirely and sell individual tracks instead of albums, which at 99c per pretty much killed the enthusiasm for stealing.
Throwing it out there as something to compare to. People still pirate music, but there's no longer a market pressure for someone to automate it, other than odd Ukrainians. It's only when that piracy became easy and anonymous that it went wild. Right now Snapchat is user anonymous, but takes user interaction per picture and is owner monitored: most users don't have any incentive to go stealth. Snapchat is in the era of recording songs off FM Radio with way better metrics.
Short version : Why push something to go underground if it's working within reason?