I leave mine in because…
I have had 2 instances of total brake failure, last year in a vintage race at VIR I had a front caliper "break", of course this happened going into turn 1, I ended up on the other side of the tire barrier, on top of the armco. They had to get a boom truck to pick the car up, I left the track at top speed, if I did not have the hand brake, I would have been in the swamp, I was able to get the car spinning and scrub a lot of speed.
The 2nd was in the Pittsburgh GP, crossing a bridge you are headed straight towards a statue of that Carnigie dude, there is a 90 degree right, surrounding the statue is jersey barrier…I had a pad break in half and come out of the caliper, I jack the handbrake, did a rally bootleg turn and went back to the pits to change underwear.
Brain’s post about trailering is very correct, drive the car on the trailer and set the brake, saves your trans from rocking in gear when you strap it down, also safer as you can kill yourself when it pops out of gear while you are exiting.
Al