I own one hard tooth saw, bought for outdoors. I don’t use it, as my Disstons do a better job, and quite easy to keep in tip top shape!
agree - my only exception is pull saws. Stanley makes a decent 12 tpi carpenters saw, or at least used to, that's 26 inches long, but the first one i had, a tooth caught one way or another in a cut in ash (no metal, ...hard ring or some grain or knot that just happened to be a destroyer? don't know)....I dutifully pitched that instead of saving it for later for something that I don't need, but would like to grind it up and see how good of a scraper it would compared to other floppy thin blades that weren't very good.
BUT, even that stanley is hard on the back side of a cut and it's far better just to file a regular crosscut saw a little aggressive (less fleam) if a crosscutting "break down" saw is needed for new boards. The idea is fine with the tall teeth, but I've never packed teeth on a carpenter's saw. I have, however, loaded teeth on a cheap dovetail saw with rounded gullets. But that's not for this discussion.
2 or 3 years ago, I bought 24 Z 260 or 265 crosscut blades from japan for <$5 each. At the current exchange, they'd be <$4 each. They're handy to have to stuff something in a metal vise (like an exotic for a knife or tool handle) and just wail away without the room to use a "good" push saw.
For regular woodwork, I have trouble finding a use for the pull saws, though - at least the disposable ones.