[dahart]

What better error handling can one do without reserved special numbers?

Many (most?) compilers already offer a “fast math” flag that foregoes denormals. You don’t need to remove denormals from the format in order to avoid them.

Having a separate type without specials would probably cause unending confusion and increase bugs. It’s already the case that only people who care about the specials handle them, but it sounds like there are more of those people than you think, if you think only mathematicians care about them.