Why isn't this a thing already, just like hotels, pre-authorize a minimum table charge to a debit/credit card (ensure AVS and/or names matches - most CC processors fraud systems provide this info - so you have correct details to blacklist in the event of a chargeback) - infact actually the reservation provider should be handling and swallowing the chargeback risk - they have the aggregated data and taking a big fee for essentially a risk free SaaS.
They probably don't want to raise the bar any more for potential customers: too many hoops and I'll just use the phone instead; it'll take less time to call than type my CC#
The idea would be that they do the same on the phone, it's much easier to type than have someone try to process a CC over the phone 5494 2442 what was that again 5494 242.. etc.. It's almost impossible to secure a hotel without a CC nowadays even for pay on arrival, it will take some first movers but I'd suspect most would follow suit pretty quickly.