In practice, I find that my car kit is split into several "kits."

Mechanical kit: the usual suspects that keep a car running, deal with minor breakdowns, keep it visible in a pickle, and facilitate a dig-out or pull-out from a ditch or snow bank.

People kit: keeps people warm, hydrated, first-aided, crudely fed, and well-communicated with the outside world. Includes a few spares for people also stranded but practically naked except for a smart phone.

Deep 05H!T kit: this supplements the kits above; some is readily accessible and some is packed in around the spare tire; typically includes a short, indestructible axe, a surplus SWAK-knife or multitool, vise-grip, saw, a decent sized pot, firemaking gear, and other things a dayhiker would normally carry.

As well: I try to have a selection of key items in a daypack that I can toss in the trunk of someone else's car (which for various reasons ends up as the transport of choice). I always get a fair bit of chaff about this, but I pay little heed, since nobody turns down the gear when they need it, so they're just blowing smoke.