You could, for sure. I'm not keen on leaving a key in the car, but you could certainly duplicate it and store it somewhere safe.

In terms of cloud, I'm currently building a product for this. Initially not self-hosted but working towards that option and the fun UX things we can do like key sharing to a family member etc.

Regarding "house burns down" ... couldn't you just duplicate the hardware wallet and keep it in a vehicle or another third location?  Is there a threat vector there that I am missing?  Are you self-hosting your "cloud"?