I've seen the F18 guys trailer their boat backwards on the trailer and I'm wondering if anyone with a 16 has done it.

To me, it seems like it would solve all the problems of having step-ladders and tripods when solo-raising the mast. Just slide the mast towards the front of the trailer (while still on the mast support) and pin it. One might have to use a few pulleys if they want to use a winch at the front of the trailer.

Is there a reason why this wouldn't work?

Except for your vehicle being in the way, and the potential of dropping the mast on it. Is the reason they put them on backwards for the spinnaker pole, to leave it on the boat?
I've wondered about putting a H16 on backwards for long drives. Just so the angle of the is backwards. Less wind getting under the boat.

It will depend on your trailer and the position of the trailers axel as to how the weight balances. with a 16 you will leave the rudders on. You just have to make sure the trailer tounge is long enough so that when your tow vehicle is at 90 degrees to the trailer that you don't smack the rudders with the car. I use a trailex trailer for a Hobie 16 with a Dart 18 and trailer the boat backwards. (properly from my perspective) The mast raising is straitforward just as you note. Push the mast forward in the front mast caddy. Pin the mast. hop on the tramp, raise the mast, have some one pin your bridle and forstay.

The down side is that if the mast ever drops out of the caddy as you push it forward ... you dent your car's trunk... big problems if you every drop the mast when you are lowering it.