That's not enough.
Why isn't it? Do you have evidence that there are a plethora of users who tip over the threshold and begin making a bunch of bad edits that need to be rolled back? Even then, the proper action is to roll them back and notify them of their mistakes. That's why those features exist. If their behavior gets extraordinarily bad, then flag for a moderator to take action.
There are many examples of 1k+ users having their edits rejected.
Those aren't really "good" examples. Suggested edits tend to be held to higher standards than regular edits, requiring approval from multiple other users. They even have a minimum character limit that doesn't exist for users with full editing privileges. In cases of edits being rejected as too minor, those edits aren't necessarily bad but just don't address everything in the post, and they certainly shouldn't be held against the user in question.
I suggest taking the suggested-edits history into account before giving the user the ability to edit without peer-review.
A reject history is not necessarily a bad thing. Hopefully, through the rejections, the user has learned from their mistakes and improved the quality of edits that they're making. Users who get too many rejects get banned for a while which is a big indicator that their actions require improvement.
For those complaining that they never see them, that's a flaw of the system. I don't see how making the privilege more complicated with something like this is a "solution" to not giving users proper feedback on their rejections.
There can be a minimum number of suggested edits with a minimum percentage of accepted edits.
This completely ignores users who just plain don't participate in the suggested edits system as frequently as others. Just because they've only made a few edits since they joined doesn't mean they're not qualified to make more edits. You also don't account for the many, many users who reached 2,000 reputation before the suggested edits system was even put into effect and wouldn't have much of a history at all (aside from tag wiki edits).
Sorry, but I don't find a user's suggested edit history to be a good indication of their editing abilities, nor have I seen any evidence that the way things currently work is causing any noticeable harm. There are probably just as many users out there that would qualify under these terms making bad edits to posts that need rolled back. What do you propose we do to stop them?