At least eight or ten people replying to this thread!
Myself included. Good volume of air, proper connections directly to battery. Decent carry bag. Compressor could even be home-hack permanently mounted under the truck, with an air hose extension to a chuck.
If going that route, one should be competent in 12V wiring, and consider that the compressor itself may not have been designed to remain in a permanent, under-truck environment... but it could be done and it would work well enough in favorable conditions (stay off saltwater beaches, etc)
I use mine then package it back in its carry bag. I use it a lot, too. Cheers.