"Why is coral allopathy preferable to assumed but not proven algae allopathy?" - its not, who said it was?
I must have misunderstood you because I thought that was the gist of the whole thread(macro algae was bad because of allopathy). I have algae living side by side in my tank without any negative effect on the coral. One cyphastrea is actually out competing the algae.
"assumed but not proven algae allopathy" - what proof do you want? Observational studies, experimental studies? Yes!

Controlled scientific studies would be good, was there one linked? Sorry I missed that.
"I tried more grazers" - without grazers on the reef, algae takes over even with optimal water parameters - in our tanks it can be even tougher because we'll get overrun before a suitable type and population of grazers can be found. Sometimes you have to be the grazer.
Many, many marine algaes use sulphate to build stores of reserve nutrients to weather periods of limited nutrients. I'm not convinced that absent grazers you can starve algae into submission without starving your corals as well.
? Corals thrive in "nutrient starved" conditions where algae is not growing. I've been able to see my algae problem drastically reduced by reducing nutrients while my corals have improved. That certainly isn't the same as eliminating the algae but it's approaching submission (I'm sure I saw a white flag from some turf algae last night, LOL). Being the grazer can be tough. I didn't think about that when designing my scape. I can't remove rock to manually remove algae because they are connected in large chunks. But I do my best to manually remove algae where I can.
"What coral grows fast enough to be effective at nutrient transport that most would want in their tank?" Does it have to be a coral - clams sequester nutrients - dursa grow very fast - I expect I can export several large BTAs from my system per month...(I've had palys which grow almost as fast as algae - but with the same allelotoxic issues and no I don't want them in my tank.) Coupled with water changes and isolated (in my case sulphur) denitrification - as its not a closed system, I control my nutrient levels easily.
I don't want Xenia, clams or nemes. I want to keep fish that aren't compatable with clams. I don't want Xenia for some of the same reasons I don't want algae. Anemones...probably will have one but I certainly don't want a tank full of them. I want a display tank ....not one where I'm using the whole tank as a nutrient export tool. I'm sure it's possible but that's not what I want my tank to be.
"the only thing that helped was GFO to get my PO4 down to 0.02-0.05 and carbon dosing to get my nitrates down to 2.5-5." I think you're phosphate reduction did the trick. No need to keep nitrates that low - doesn't hurt but isn't necessary either.
I think your're right. I cut my carbon dosing by 2/3 to keep it around 5 where it is now.
Carbon dosing has its own issues as carbon limitation holds bacterial populations in check. Disregulate these and you'll bleach or stn your corals.
I agree with this also. That might very well result from a dosing accident with malfunction of a dosing pump/owner-operator error.