However, making such edits would bump many posts, which leads community leaders to withdraw their decision.
Your leaders sound like a rogue clique that want to bypass the rest of the community. If they truly are leaders, I'd expect them to be well-versed enough in Stack Exchange etiquette (after all, they are leaders, not just any random user!) to know that any such edits should be discussed on a site's meta site first. Not only to gather input from everyone that wants to provide such, but also because sometimes, moderators or SE employees can help out with such edits.
If the wider community is aware of this effort and it is approved on the site's meta, you can go ahead and edit. There's no need to 'withdraw their decision' just based on the number of posts it would bump if people agree these are good edits to make.
Problems arise when your leaders end up being the only ones deciding whether to edit or not to edit. If they can't bring up the decency to post on a site's meta and discuss the changes, they're not really leaders, just a clique. And then yes, people will wonder why so many posts are being bumped on the frontpage, and why no one asked if this really was necessary before doing this.
The Stack Exchange community team disagree with not bumping minor-edited posts to prevent malicious edits.
Not just the community team, there are probably plenty of people out there who agree with them. Like me. If people could hide their edits, that means editing becomes much more open for abuse. Even if edits aren't outright malicious, from time to time edits do not improve the post, or the community disagrees on what should and shouldn't be in the post.
Again, if your leaders have discussed their edits with the entire community, and gotten approval to start doing these edits, there's nothing to worry about, because the community knows these posts will be bumped. But edits that bypass this process might be labelled as malicious, and all your feature does is help your clique of leaders get rid of some oversight. I don't want to have to rely on users having to keep track of edits in an extra list to see malicious, wrong, or superfluous editing to flag them. Just bump them, your leaders need oversight as well.
We can add the option "organizing edit" in the editing environment of posts so that a certain group of community members, who are already selected by community moderators, can use this option to make required edits on a set of post.
At least, this selection of users shouldn't be manual: All that does is add overhead, because you need to manually check if this person really can be trusted with this option before allowing them.
It's also not necessary if your group leaders follow the right process for these edits: Discuss them on meta first. After that, it no longer matters who makes the edits, anyone with editing privileges can do so.