This sort of feature would almost certainly have to be network-wide, so Super Meta may be a better place for this request. But here's my take anyway.
Don't allow new users to edit
Strongly opposed. There's a huge swathe of edits that you don't need a lot of experience with a site to handle; the spelling and grammar example you give is one. There's lots of value in letting low-rep users make some trivial edits. Even anonymous edits have value; 41.5% of anonymous suggested edits have been approved.
Sure we probably could let the high-rep users handle them, but why?
Give high-rep users a weightier approval hammer
Some variation on this has been suggested a bunch of times before, notably:
Three drops in a veritable tsunami of examples. The usual response given is a historical one; something like this was tried out on StackOverflow a yonk-and-a-half ago, and it ended up spamming the site with a bunch of really bad edits. And while I'm not personally convinced by an argument from historical experience, there's another argument I like, made by Servy in an answer to one of those Meta.SE posts:
The suggested edit queue has demonstrated time and time again that rep is not a very good indicator of the quality of the reviewer. There are lots of reviewers with a lot of rep doing a constantly poor job reviewing.
Maybe this isn't a problem on SFF; I don't know. I do know there have been times where I've disagreed with the outcome of a review, so having another set of eyes isn't an inherently bad idea.
I might support this more if it were tied to something more indicative of review experience; maybe you get a hammer with the review queue or editing badges , or something. But even then, I mean; I have three (almost four) gold review queue badges, all six review queue silver badges, and the gold and silver edit badges1, and there are still times I want another set of eyes on one of my reviews.
But there is one aspect of the suggested edits queue that I think is a bit silly, but I'll cover that next.
Let us override suggested edits
Unless I'm radically misunderstanding what you mean, we kind of already have this: it's basically what the "improve edit" and "reject and edit" buttons are.
In principle you could improve a suggested edit in an extremely trivial way, say by adding a comma somewhere; the original edit is automagically approved, and the user who suggested it gets the +2 rep.
Alternately, you could choose to "reject and edit", and just make all of the same proposed changes again; the edit is automagically declined, and the original proposer gets no rep.
I think that's a bit silly.
I'm unsure what, if anything, would work. A couple thoughts off the top of my head:
Reduce the reviewers required on trivial edits. Problem is there's no easy way for an automated tool to determine triviality, but still protect us from destructive edits being approved by lazy reviewers; it doesn't take much to introduce vandalism or profanity, and having only one pair of eyes on an edit like that leaves us very susceptible to robo-reviewers
Give certain badge-holders a suggested edit hammer. I don't know how difficult this would be to implement on the SE platform, but it seems reasonable enough on the face of it; we give a dupehammer to gold tag badge holders, so why not give a smaller hammer to someone who has, say, the copy editor badge?
One issue I see is that edit badges aren't tied to contribution quality the way tag badges are; getting a gold tag badge is rather hard (unless you're Richard, who seems to attract them magnetically), because you need to demonstrate a volume of quality contributions. The edit badges satisfy the volume requirement (500 edits is rather a lot), but not the quality requirement (there is a minor quality baseline, since rolled-back edits don't count, but that's negligible). In theory, you could get that badge with 500 one-character edits, and I would not feel comfortable giving a hammer to the person who did that
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