So why so little mention of 1 inch belt sanders
for sharpening curved profile tools?

I've used them and they are sh*t. The vibrate like h*ll. Also, belt grinders
don't grind flat. They have a tendency to grind convex surfaces, and they are
prone to sniping. Just like a planer can snipe the leading and trailing edges,
so do belts, even if tightened.

Case in point. A pattern making shop I used to do business works in mahogany.
Lots of big woodworking machinery including a huge 30" x 8' pattern makers lathe
with compound tool carriage. I asked them about belt sanders and they said they
tried one and sold it. What they use to grind flat surfaces in wood is 24" and
30" disc sanders.

Nonetheless, I do sharpen with belt sanders, a 2" Grizzly knife makers machine.
Very nice, very smooth. I also have a Baldor 8" buffer, 6" grinder, and a Darex
tool point sharpener. I think you need a variety of grinders to do the job.
Dan

PS: Tool Gloat: That pattern shop had a "little" 2HP, 18" disc sander that they
didn't use much because it meant they had to stock another size of discs. They
GAVE it to me!