The 10 1/2 carriage makers rabbet plane is one of my favorite tools. What part of carriage making required a rabbet plane with a 2 1/8 cutting width I have no idea. In my experience, they are not a particularly great rabbet plane, too wide for most of the stuff I do. Where they do shine (at least for me) is fine tuning large tenons in my workbench classes. Planning cross grain, the 10 1/2 can quickly and accurately size large tenons cheeks with ease. The full width iron allows you to work right you to the shoulder of the tenon, which is nice.
So what is the hiccup with the tool that makes me not like it? The arches over the mouth of the plane are weak. The brittle cast iron vintage planes are made of makes the situation even worse with this tool. Many of these planes when you find them have had repairs such as welds or scabs riveted on the sides to hold them together, most times rendering the plane almost useless. The unbroken examples fetch pretty good prices because they have become collectible and harder to find nowadays.
The No. 10 and No. 10 1/4 are also available (10 1/4’s are made new by Lie-Neilson), all three versions share the same width iron but the 10 and 10 1/4 are longer, heavier and a bit unwieldy for sizing tenons.
My luck with the 10 1/2 has not been that good, had one that was stolen during a class, one that got broke. I continue to use the two I have for now because they are hard to beat for the big tenons on workbenches. Hopefully sometime in the near future these will get reproduced in a ductile iron version, making for a less worrisome tool to own and use.