Do regular service intervals influence this? Would Tesla improve the safety of their cars (by this metric) by giving a regular service for safety items in tandem with the safety inspection interval?

Damage done by the driver is one thing (AFAIU, Tesla Service pricing is pretty damn competitive for repairs), but warranty work like light alignment and function, premature suspension wear (big on Teslas), and brake maintenance probably don't make a difference to Tesla if they are done before the safety inspection or after in terms of cost, but is rather important in terms of reputation...