Breeching is always such an interesting issue.
I'm a great fan of it and use it almost all the time but then again I do a tremendous amount of trail driving and cross-country work where it would be nearly suicidal to go without it. It is standard equipment on a carriage driving style harness just as a check is standard on a fine-harness style turnout.
I think what's important to remember is the reasoning behind any given piece of equipment and to evaluate whether that reasoning applies in your individual situation. It is my opinion (and my opinion only) that fine harness with a miniature is a different deal than fine harness with a Saddlebred. Saddlebreds and Morgans and such may be 16h and hauling this little tiny jog cart behind them, something which weighs maybe 1/5th of what the horse does. The shafts are strongly downhill to the cart and the shafts are usually snugged tightly to the saddle with French tugs or wrap straps and often thimbles on the front. The weight of the cart is well over the wheels and the slope of the shafts gives the horse pretty good control of the vehicle for stopping and turning. Backing is not that hard because the cart is light compared to the horse and the wheels are usually large enough to stay on top of deep arena footing.
For a miniature, especially an A-sized one, none of those things are the case. You've got a horse who weighs maybe 200lbs (give or take 50lbs) hauling a cart which weighs 80lbs or so plus a 150lb person. The shafts are at best only slightly uphill so a lot of that weight is often on the horse's back and with the shafts tied down tightly, there is a load thumping up and down on the spine and the horse does not have a good ergonomic way to brake or turn the cart. When stopped in a lineup those tiny 20" wheels sink right into a soft surface and then you've got this little tiny horse trying to shove something straight back using only his withers- not a comfortable situation! I'm not saying they don't do it and do it just fine, but in my mind it is not the same situation at all as that of a fine harness Saddlebred or Morgan. There are totally different numbers in the equation.
So, that said, what variables can modify that equation? Well, having a bigger horse for one. A B-mini or Shetland comes closer to the ergonomic setup of a full-sized horse and will have less problem. More muscle, more height, more weight in comparison to his load...you get the idea. The single biggest difference I've seen between a panicky, unhappy horse without breeching and a calm, perfectly contented horse without breeching is the way the harness is adjusted. Too many times I've watched beginners hitch up a horse with no breeching and a tight overcheck to an easy entry cart and proceed to drive around the ring with the cart rolling up almost to the horse's hocks each time they stop. This of course loosens the traces to a dangerous level (the horse could easily get a hind leg over them) and then when the horse walks on he's a stride or more into it before he suddenly hits the traces. He wants to stop, the cart starts to roll up on him, the person smacks the lines on his butt and he jumps forward, hitting the traces again and causing the cart to roll forward again....Oy. These horses always look terribly stressed and I can't think that's a comfortable way to drive. However I've seen other people with the same cart and harness setup who have things adjusted so that the cart stays safely back, the traces stay safely snug, and the horse can round up into that check (or better yet the driver's hand) and their horses do just fine and are perfectly happy.
For the first person breeching would be my solution to keep horse and driver safe as the driver learns how to ask for soft transitions and how to correctly adjust the rest of their harness. For the second person, well, if they prefer to use fewer straps then I guess I don't really have a problem with that.
If you are going to drive without breeching (and this is a general statement for all readers, not you specifically Mimi,) then PLEASE be prepared to put shaft stops on your vehicle! Even the tightest of wrap straps can slip and without a physical projection on the shaft to prevent it from slipping through the tug loop you are endangering your horse and yourself. Having the cart roll up and hit a panicked horse's hocks each time he tries to obey and stop is the kind of accident many driving horses never recover from. IT ISN'T WORTH IT. Nothing is worth it when a cheap piece of hardware could completely prevent the problem.
My final thought on the subject of using breeching for ring driving is to respectfully suggest you include the breeching in the initial training rather than adding it later. It is very easy to take the breeching off and continue to drive the horse with no further lessons, but a horse who has been driven without breeching may object rather violently the first time he feels something pressing on his rump. Margo C-T shared a story a few years ago about an experienced show mini that went trail driving with breeching for the first time and the resulting wreck was not pretty. It is better, in my mind, to introduce the breeching with all the other new things at the start so the horse accepts it as simply part of the deal.
Leia
P.S.- If you haven't considered using a bucking strap on your green driving horse, do a search on the forum for "kicking strap" and read up on it. It's a great safety device and can be used with or without breeching.