Part of the problem is, we've "all" kind of got obsessed with Action Cameras that were designed originally for the opposite of how we use them, and what we want. To the extent, that enough petrol/gear heads use them now on cars and bikes etc, that the makers have tried to throw us a bone by including some software features that work well for us, image wise, and clamps and mounts suitable for vehicles.
BUT, we still have the issue that the actual cameras are designed to be miniature, all in one devices, easily worn on the body or head, for shooting action sports footage. So they're not designed to have permanent power supplies, or constant running.
There are cameras designed for vehicle use, which have much better focal length lenses for car to car filming, permanent power supplies, proper remote stop start buttons etc. BUT, because they're for such a small market, the prices are huge, fitting is more complicated, and frankly the technology lags behind the action cameras quite a bit.
You're probably almost as well, for what requirements and price you list, just looking at the really cheap knock-off clones of Go Pro's etc, and regarding them as almost disposable. - And lots of batteries/memory cards.
Or, go for a second hand decent camera system, from maybe a generation or two back, when someone upgrades to something newer.