I find this nothing but a distraction. If you can trust users enough to let their flags have an immediate effect, you can likely also trust them enough to simply hand them a spam handling ability.

We can also add an ability based on, say, "5 approved flags and flag-approve-rate > 75%" that enables the automatic link suppression on posts they flag.

You're pretty much advocating for a new ability in our system here, and I don't think that's helpful when you take a step back and look at the whole picture. The issue remains that flags are not handled fast enough, or that positively contributing flaggers don't earn the ability they should be getting.

Additionally, you're giving abusive flaggers a tool to effectively temporarily shut down parts of a post. This can be weaponized, and much more effectively than an otherwise very disruptive action such as posting. Because posting is so much more disruptive, it's also dealt with faster.

I also don't like how this would enable people a way to anonymously attack another user. Imagine user A has a set of posts, and user B starts targeting them with false flags. User A may very well notice the attack before a moderator invalidates the flags, but never find out what's been going on. I'd not enjoy being in the shoes of A. Additionally, you're allowing B to put a public label of shame on A. That in itself can persuade viewers into thinking the accusations are fair and correct. They'll just see that the website labelled A's content as being against the rules. They won't look into the details themselves. So yeah, I also don't like the way that this can damage the reputation of A.