Usually those "low quality posts" are:
- Answers that really are comments (score 46 example, score 46 example), but those are getting handled separately.
- Poor questions (score 43 example, score 49 example), but those can get closed.
- Hastily written answers (score 29 example answer, score 52 example answer) that can be turned into useful posts by some expansions or some linking to documentation.
The edits to the third kind of posts can be rewarded easily without having to vote on edits.
You would, for example, gain 1 token reputation by improving an answer's score by 10 points* (and lose as much by making it worse, so that you can't do rollback wars with yourself.) This reputation would count towards the rep cap. Closed and CW posts wouldn't count.
This doesn't need to only apply to bad posts. This would encourage tasks such as editing an incomplete answer, instead of adding a competing one (as much as it is encouraged, I think one good answer is better than two possibly incomplete ones) -- from what I see, just making a post longer improves its score.
The Stack Overflow only problem with this example is that, on average, adding code reduces a post's score. This could result in a reputation penalization for adding code sample to an answer! Similar problems may also apply to LaTeX sites if the score calculation counts equations. We're talking about 1 rep however...
Also, this may make reputation recalculation more expensive -- especially now that you can make them on-demand.
*Average edit score gain in the few tests I've made.