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From a skate tech point of view, parabolics require fanatical attention to detail during mounting, because the thinner cross-section at the middle makes it very easy for the blade to get pulled out of alignment while tightening the mounting screws. I think the biggest problem with sharpening parabolics comes from the likelihood that the centerline of the blade does not run in a straight line down the boot, in which case no matter what you do, you can't get the edges level along the entire length of the blade. If they are mounted correctly, and they are not also side-honed, they will be more of a nuisance to sharpen than a standard parallel blade but getting level edges is possible.
I know there used to be options for blades that were both side-honed and parabolic, but I'm not sure if that is still a thing. I'm happy to say that I have never handled a pair, and they seem like they would be a nightmare in terms of finding a consistent datum for finding level. It's common for side-honed blades to be tapered from front to back (Wilson Gold Seal, MK Gold Star...) but not hourglass shaped. I've wondered whether the taper is actually the defining performance feature on the Gold Seal, because on most Gold Seals and Gold Stars that I have seen, the chrome relief band flattens the flared edge (or even angles it the opposite direction in places), so you don't truly have a flared edge, but you still have blades that are difficult to create level edges on. Seems like the Pattern 99 with parallel sides would give you a more consistent experience.
I am hoping to do some of the same experimenting with different blades that Bill did, now that I have had my boots rebuilt and my old boots can be experimented with. Now I "just" need to find the blades...