That's literally what they're doing:

For starters, Mastodon says it will allow users to control whether their posts can be quoted at all. This would protect people from being the recipient of unwanted attention or hateful replies to some extent. (Though, arguably, people could still screenshot someone’s post to circulate it more broadly if they intended to troll the user.)

In addition, users will be notified if someone quotes them, and they’ll be able to withdraw their post from the quoted context at any time. This latter option could help in the case that someone’s quote post goes viral, and the original poster starts to receive too much attention or even abuse, forcing them to reconsider whether they want their post to be quotable at all.

I think you'd need a little more than that to make sure the restriction isn't used defensively by harassers (one of the reasons people ask for this is to show others bad behavior in their replies). But it does feel like a solvable problem.

And Mastodon having more active moderation (since you can proactively look for an instance that meets your moderation expectations) also means the stuff that can't be handled mechanically can be managed.