I think it would lead to a lot of posts written specifically to be Liked and - possibly - people holding back on a post that might not be Likable. If you want to keep that ratio high, you can't waste time posting something that's not eligible for a Like.
Basically, I think that in a fairly short period of time you'd have a preaching-to-the-choir situation.
The magic of Like is its simplicity: someone read your post and appreciated it in some way. I don't get why anyone would want to mess that up by using it as a popularity meter of any kind. What exactly do you gain by trotting your popular members around the show ring, except to give the great Unliked masses the impression that they aren't valuable members of your forum?
I hope all these Like suggestions are Mods, not built in.