In most cases, the "like/post ratio" would be less than one, making the trophy points virtually the defining characteristic of your "reputation system".
The purpose of likes, in my opinion, is not to act as an indicator of post quality or member popularity per se - although at times it can do both. It's really a behavior modification device used for increasing member interest and participation and the results will vary widely depending on the nature of each individual community. Like/post may be useful to some, but probably not to most forums.
The complexity of a true reputation system is probably contrary to the XenForo experience.
Abomination, I think that liking posts because you agree with something would happen less on other forums. Perhaps you could disable likes in some forums to count towards the ratio, and I agree with Sandman. For some sites it just wouldn't work at all so like for any feature it simply would be a choice whether you use it or not.
If the like/post ratio somehow increases interest and participation on a site above and beyond the standard like functionality then it could be worthwhile. I don't think it could or should be used as a substiturte for a reputation system.
Likes are what they are, and I personally see no need to manipulate them and make them something they aren't.
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.
I completely agree with this. The magic is that it extremely simple. Simple is good, especially for people that have many things to do and don't hang out on forums all day, many visit a forum to say hello or exchange a bit of information, then come back at a later time.