Good question. ALWAYS understand what you are doing before you do it!!! Just because breed show people do something one way does not necessarily make it the right way. Like Marie (Shortpig) said, you really should use breeching in the real world. It is a much safer, more comfortable way to slow and stop the vehicle than any other "accepted" way for minis. Mechanical brakes would be another one, but not for a two-wheel mini cart (four-wheel maybe), which adds downpressure on the horse's back in the braking process.
Breeching uses the horse's big meaty haunches to slow and stop the vehicle, whereas thimbles and wrap straps use the horse's girth and bony withers to accomplish that. Would you rather stop a wheelbarrow with your butt or your shoulders and armpits? The reason show drivers don't use breeching is because they "don't want all that leather on the horse" and that is the way the big horse show drivers do it. However, the weight ratio difference for cart and driver with a big horse vs. a mini is tremendous! The big horse isn't nearly pulling or holding back that much weight!
IMO, it is a disservice to the horse not to use breeching, no matter what the trend is in the show ring. But, obviously my opinion is not the popular one from your observation.
We used to use thimbles and wraps straps. Now we know better, so we do better.
Myrna