SoCal - no, UK rental agreements usually include full insurance, with the renter paying an "excess" - the first £x (typically £500-£1000) of any damage.
From a UK perspective, US "renters insurance" is a hidden charge we wouldn't pay at home.
I've never heard of a student being banned after a solo accident - I do wonder if there is other information we don't have, such as the student's manner and attitude during the inevitable post-accident interview with the CFI.
G