First, a clarification, the change in the DVLA is for the paper counterpart to the photo id licence, not the paper licence that existed before the photo id licences. Many people will have been switched to photo id by moving house though, so it’s only the hardcore who won’t be included.
I got confirmation from the car hire firm 24 hours in advance that I needed to print out my endorsements sheet, by which point I no longer had access to a working printer, so I was glad I’d tried it beforehand. The guy at the desk noted that it was a new scheme, and also mentioned that if I hadn’t printed it out, they would need to call a DVLA verification phone number which is very busy when it’s not shut. So still a number of teething problems to sort out.
Do if you are hiring a car, get yourself over to dvla in advance (any time within 21 days) and get your endorsement sheet printed. It might just save you from long queues and grumpy car hire staff.