You need something to manage your clients on that network. If your modem can do that, good, you may not need a router. If the modem can’t or it is not setup-ed and you can’t access it, then you most likely would need one.

Here is a dependability study in the US

https://www.jdpower.com/business/press-releases/2023-us-vehicle-dependability-studyvds

Doesn’t really answer your cute question, but it’s still info.

Complete engine failure is quite uncommon. The question is about complete battery failure, I hope would be the same uncommon, but no actual stats or observations