It's not an acronym I'd ever use (and I'm pretty sure it goes back before the WotC boards - I know I've seen it on non-gaming boards before), but it doesn't annoy me too badly. I do think it's a little too "cutesy" which might rub people the wrong way.
I don't think the "please" part of the acronym is a problem; I'd have no problem if someone put up a suggestion and said "Please critique" or "Please let me know what suggestions you have to make this better" or something like that. The "please" is nice, in my mind.
The "honestly" part isn't too bad either. I'd interpret someone who spelled out, "Please evaluate this and offer me your honest critiques" as saying, "Don't spare my feelings - if you really think it's awful, please say so honestly." That's not a useless thing to say; people do sometimes hold back or try to phrase things nicely in an effort to spare someone's feelings (yes, even on the Internet).
So, while I don't really like the acronym due to its "cutesiness" I don't have any problem with someone actually spelling out a polite request for honest feedback.
I just think it doesn't need saying. It's implicit in any posting of your own material; add the horrible cutesy aspect of it you mention, it makes me cringe. I don't see any need for it (and, indeed, I can see that it implies to some that the reader would not be honest otherwise - though that's not an implication that I personally infer).
I'm not gonna stop people using it here*. I reserve the right to mock them for doing so, though! And I personally will refuse to participate in a thread so labelled on a point of baseless principle!

*Unless it becomes endemic and starts to really irritate me.