A little OT, but drivers license in Ohio are laminated?!?! Texas uses to have those about 15 year ago, but they lead to fake IDs being created (delaminate and swap photos, etc). Now, as with California, Texas DL is hard plastic with a 2D barcode on the back.
Back OT, I think the stock is used on-site at the DMV vs using preprinted plastic stickers is due to cost. Registration stickers are replaced once a year anyways, and they can be sourced online mail order or at any DMV office. So cost, availability, and time of delivery are minimized. The UK might want to adopt this method too.