This is not a big deal, but we get a fair share of questions in the "reopen" queue where the edit is done by some well-meaning user in order to fix spelling, grammar or formatting without touching anything that made the question closed in the first place.
It is very rare indeed that a edit by anyone except the OP fixes fundamental problem (after all, it is really hard to guess what the OP meant in the majority of these cases).
It would save us some time if a question only got automatically reopened for voting if it was edited by the OP.
In addition, those with enough rep can always nominate for reopening if they think the edit fixed the problem (those without the rep get their edits reviewed by those who has) If this gets implemented, it will probably be a good idea to lower the rep for nominating for reopening to the same as the rep required to approve "suggested edits" . i.e. 2000.
To put this in perspective, I just reviewed the last 50 items in my "Reopen" review queue (we do not all get the same items for review, so you may not get the same figures as me). Of those 50 items, 47 are still closed. Only 3 (6 %) was reopened. I then examined the 3 items that were reopened. Each and every one of them (100 %) had been edited by the OP.
While the above probably has too few data points to make conclusive statistical evidence, it doesn't look like we'd lose a lot of deserving candidates for reopening by only considering those either edited by the OP or nominated for reopening by another user.
PS: I'm mildly amused by the notion that lowering the threshold for nomination to 2000 for reopening deserves a second downvote, but the same person seems to be perfectly happy with the fact that today, rep 2000 users already can nominate for reopening just by making a trivial edit.