I'm asked to do this occasionally and my response so far has been -- not for the rate your paying! Seriously, does anybody really agree to do this? I consider it dangerous for one thing, not to mention the indignity of it. I'm just not of a mind to get stuffed in a trunk driven by an actor whose attention isn't properly on his driving just because they're too cheap to pay for a process trailer. Is this unreasonable?

I agree with you. The trunk (of a modern car) is a crush zone that's designed to collapse and absorb some of the energy of a crash.
In an older car you'd still be unrestrained and in a bad position during impact. There could also be greater chance of an exhaust leak with an older vehicle.
In some (most?) states it's not legal to ride there anyway.
It's just a bad idea, but it does get asked.

Why do you have to get stuffed into a trunk?

And if you do, why isn't there a professional driver at the wheel under controlled circumstances?

Do you ever get in the trunk? I used to do this ALL THE TIME.

To get into Drive In movies underage. As a working pro? Please...

"Isn't there a professional driver at the wheel under controlled circumstances?"

Sadly, this is never the case. Situations where they want you to get in the trunk include when the car is just too full (two actors, director and DP already sitting up there). In the past I've handed the director the mixer and said "do yer best pal!"

C'mon Shaun, I think the real reason you don't do it anymore is the same as my reason - we wouldn't fit:<)

(Just kidding)