I can agree that popularity and reputation interfere. But it is difficult to place restrictions on reputation, for many reasons.
Reputation is something that can drive a site. People like to receive appreciation. It may be a bit of a sad truth, but there are many examples out there. Just look at reddit or imgur. People fish for upvotes as if it is real money. And trust me, people go crazy over reputation/upvote injustice over there too. By nature, those sorts of systems are imperfect because they rely on user input. Users cannot be controlled. Restricting them more and more will only lead to dissatisfaction.
Regardless of morals, reputation plays a role into people's motivation to help. While that may be perceived as bad, it is kind of nice for the site as a whole. You hardly have threads without any replies (except in requests). New users also get some motivation to stay on the site (in any help forum, there are "one-and-done" posters). Now, I know you aren't saying to remove reputation or anything like that, but any changes must be weighed carefully so that they don't demotivate users.
It is possible to restrict it to more sections, but since all sections apart from off-topic have potential for "valid" reputation, I don't think that is necessary. As for restricting who can give rep (the thread owner), that may be detrimental considering there are a decent amount of forum-goers (myself included) who admitted to giving reputation to posts that have been helpful. Nothing is wrong with someone getting extra rep for a particularly helpful post, especially if it helps more than one person. And if someone comes in late to the thread to help someone other than the author, it is unfair that the helper wouldn't be able to be repped.
The reputation power of 1 thing is a neat idea. But I think there are too many associated issues. It would deflate everyone's rep (which might lead to some disappointment), but it would also nullify a lot of the rewards for contests. There are a lot of contests that just offer reputation rewards rather than icons (especially mini-contests), and it would be difficult to strain those out of all the reputation that people have been given.
I agree that 1 rep power is more fair, but it is (1) motivating to users (so they can give more reputation) (2) exciting for some users. Imagine you're a street performer. It feels nice when people throw chump change into your hat, but when Mr. Big-Shot sporting a swirly mustache, long top-hat, monocle, and flamboyant pants comes in and flashes some cash, you get a big thrill. And then you become hopeful that a similar man will return again. Fair? Not quite. Fun? Probably. Maybe I just like to preserve reputation's uniqueness. When it goes down to 1 power, it becomes even more like the "like" system. But due to the fact that reputation has varying power, can actually have comments, and isn't used the same way as a "like" or "upvote" on other sites, it becomes a different entity.
As for Chocolate Bunny Points, something like that may be considered for Hive 2. There was a discussion about it, I think. It would be a good alternative solution to the issue at hand.
Although, it is always good to remain hopeful. I'm not shutting down your suggestions, because this has actually been a case in the past. Before 2008 or 2009, users needed a certain reputation level to grant reputation at all. Otherwise they would end up giving 0 (maybe to prevent rep bots)? But that was problematic because a good portion of those asking for help were newer users. It was eventually changed, for the better IMO, and I believe it made a good difference. Similarly, off-topic got its reputation restriction at some point in time. That helped restore some validity to reputation as well. It isn't perfect, but it has had some good changes in the past.
It is true that there are many cases of popularity-reputation, but I think there are even more "good" examples of reputation. As such, I believe there is still credibility in it.
you just have to look hard enough, and believe. ;-;
