I'm pretty sure it's still private charging. I know there are some kerbside charging solutions that are a public/private mix so discounted for residents but I don't think we need a lot of public charging infrastructure on normal streets. The only time I use public chargers is when doing long journeys and I stop off at motorway services which benefit from the 50kw+ CCS charging while I have a pee and grab a coffee.
I would hope in time that private charging gullys would become a standard part of street furniture when streets are renovated and redone. It's going to take awhile before the majority of cars on the road have transitioned to electric.
Not sure what to do about the insurance premium issue. I would hope some of the ADAS improvements in new cars will eventually reduce the number of battery integrity threatening prangs.
I've got an Ampere workstation (AVA) which from a firmware point works fine. They may even fix the PCIe bus on later versions.