I don't think reputation should be eliminated for this.
I recently made a large number of (mostly) tag-only edits, so I'm part of the crowd you're talking about. You can see them here.
Pre-emptively: I didn't do these for the reputation. It was a nice kicker, but I'll get back to that later. I have edit privileges on other SE sites where I don't earn rep for edits any longer, and I'd do this work all the same.
I say they were mostly tag-only edits because in a number of cases, I made some improvements where it was relatively simple, but for the most part I did not attempt to make substantial improvements.
For 79 edits I made 158 reputation.
Responding to what you said...
A certain user just got 42 reputation from removing the windows-ribbon-framework from a bunch of questions and doing nothing else. This seems very wrong, because the questions had other things wrong with them, but people were accepting the edits.
This is very emotionally charged language, and I'm not going to be able to respond to your emotions on the matter.
I'm not sure why you find this very wrong, though. 42 reputation is not very much, and it comes from doing a decent chunk of work.
I get the fact that they didn't also edit other stuff in the post. I'm not sure how to interpret that other than you feel like they didn't exert the effort to really earn that reputation. To which I say: they did expend enough effort to earn it if they were working on a tag cleanup. (If they weren't working on a tag cleanup, they're probably not the users doing dozens of retag-only edits)
As part of my tag cleanup effort, I spent a decent chunk of time trawling through questions to retag, and received ~70 reputation on each of two days and 22 reputation on one. This is not a large reward for the amount of retagging. It's not small either, it's decent. If you think it's huge, I'll get to that.
I could have made substantial edits along the way, but I wasn't interested in doing that: I was on a cleanup mission, and that was a decent amount of work on its own.
There were 226 questions under the recognition tag to work through, and that was for one particular search angle only - there's more work to do there. There are other tag cleanups that have come up that would require hundreds more than that, and a recently brought up tag needing cleanup has over 7,000 questions that would need to be worked through.
I didn't expend effort in terms of making other substantial edits, but I did exert time and effort along the way.
Not very much reputation!? (Or: Some perspective on what 70 reputation is worth)
If 70 reputation is a small amount to you, then you might not find this a problem.
To me, in the context of Stack Overeflow, 70 reputation seems like a large amount. That's Stack Overflow's problem, though, and not necessarily something other sites on the SE network share: good answers often get astoundingly little reward on SO. I've written about as much in another SE's meta: in that SE site, the average answer score is 6. On Stack Overflow, only an exceptional 6.8% of answers ever reach that mark, whilst 77.7% of them have a score of 0, 1 or 2.
In other words: whilst 70 reputation might be a lot here, it's what you might earn on average for a decent average answer on another Stack Exchange site, and those answers normally take me less time and effort than the retagging I did to earn the same amount,.
Also, as is naturally the case: these are digital interwebnet points which don't really exist that we are debating about here.
This is an OK reward. It's OK to keep it around. There's nothing wrong here.
It's nice to have a reward for this effort. I don't agree that it is wrong to earn a small amount of reputation for each retag. I think, as a low-rep user, it would suck to go to this effort and earn nothing for it, though, other than the little changes I made incidentally along the way.