I don't think the specific change proposed here would be an improvement, but this is a good question.
In the hypothetical situation you described--which is a perfectly plausible situation, considering that many low-rep users do eventually make numerous good suggested edits--I will assume for the sake of simplicity that no corner cases apply, such as edits being approved on posts that are subsequently deleted.
In that case, the first 500 of those approved edits would have conferred +2 reputation each, for a total of 1000 reputation. Since this is the maximum amount of reputation that can be gained from edit approvals, the next 500 approved edits would not have given any reputation, though the user would of course still be credited for having made the edits, in the edited posts' revision histories and elsewhere.
So those 500 rep-conferring edits get the editor halfway to the 2000 rep mark required to edit questions and answers directly without going through review.
Having had edits approved in the past is part of what predicts good edits in the future. But having general experience using the site, and being considered to have made valuable contributions in the form of questions and answers that show useful knowledge or effective research, is relevant to edits, too. As the system stands, edits can bring a user halfway to gaining the rep necessary to edit directly.
Yet it's hard to say how relevant those other rep-generating activities are, compared to a history of making good edits. As you suggest, it does seem like a user who hasn't gained much rep from questions or answers (or has but lost it, perhaps by giving out bounties) but who has made hundreds or thousands of good edits would be more likely to make good edits in the future than someone who has other site experience but very little editing experience.
But what if, in addition to having 1000 edits approved, the user also had 500 other edits rejected?
Under the feature change you've proposed, this user would get the ability to apply edits without review, based on their history of editing in a way that reviewers have judged to be about 67% good. That does not seem right at all.
Having an edit suggestion rejected doesn't take away reputation, and I don't think it should.1 But this means that to make a reasonable prediction of future editing quality based on a user's edit suggestions, the system would have to consider how many were accepted and how many were rejected. This would be quite different from the specific change proposed here. I also think it would have at least three disadvantages, regardless of how it were done:
The Stack Exchange system, which is already immensely complicated, would be even more complicated.
Reviewers would feel the need to consider the impact of their reviews on editors' ability to gain editing privileges, even though they really should not make decisions based on that.
The specific bad effect I'm most worried about here is reviewers deciding whether or not to reject an edit based on their recollections--or general impressions--of the editor's prior edits and site activity.
Editors--or, in any case, a significant portion of editors--would feel the urge to consider the impact of their edit suggestions on how long it would take them to be able to edit without approval.
This might seem good at first, but I think it would really lead to defensive editing. That is, I think many low-rep users would both select posts to edit and decide on the content of their edits based more on the desire to make it clear to reviewers that the edits should be approved than on what would actually be most effective at making the site, and those posts, better.
Often, editors don't make this clear enough. Certainly many edit summaries that I encounter in the Suggested Edits review queue could be better, and I see a number of edits that make questionable changes or that fail to make clearly reasonable changes (for example, edits that fix the capitalization in one half of a post but not the other). However, the opposite extreme is always possible. Editors should improve posts as well as possible and justify their changes as clearly as possible, but it is often good to edit a post even if it cannot be made perfect, and the edit rather than its accompanying summary is what makes the biggest difference.
However, although I think none of those disadvantages could be avoided, each could be made more or less severe by the specifics of what change were made to the system. It might well be justified to make the system a little more complicated, in a way that can be clearly documented and easily understood, and to make editors slightly more preoccupied with how long it may take them to gain the ability to edit directly, in order to make it more efficient for people who enjoy and are good at editing to make the site better.
But that would be a somewhat different proposal than simply conferring editing privileges based on some number of accepted edits, without looking at the number of rejected edits.
1The reasons I think edit suggestions should never cause a loss of rep is are: (a) The rep wouldn't be recouped by good edits made after the editing privilege was attained. This would feel unfair, and low-rep users wouldn't get enough practice making the kinds of edits they would then go on to make, so once they gained editing privileges, their edits would often be bad. (b) For answers, a downvote is -2 and an upvote is +10, so the system still encourages answers from users who aren't sure how their contributions will be judged. Even so, people on Ask Ubuntu tend not to downvote very often. If suggesting an edit could cause rep loss, new users would be overly reluctant to edit, and reviewers would be overly reluctant to reject edits, which would result in a smaller number of edits actually getting made, many of which would be bad.