The feature that mods are using is setting the subreddits to "private" (with no approved members). Disabling the ability to do this will break that function for people who use it, or look really petty.

Reddit could just disable this function on a specific moment, so that the feature cannot be used for coordinated strikes

Escalating open war against its users is not a very good idea for Reddit. Keep gaming that option out, and all the other responses and counterresponses.

Broadly, Reddit needs money to survive, and they need goodwill to get money. Burning $X of goodwill to make $10X dollars is kind of what they're trying to do now, but it's a very delicate move on their part. If you kind of build some simple mathematical models in your head it's not hard to see how delicate this move is, since "goodwill" is also people visiting. As large as the site is, it is not very many exponential processes from 90%+ losses. It is one of great perils of social sites in general, they can't help but transmit social contagions by their very design. There's quite a number of sites that have been wiped out by these forces (MySpace), and a larger number of sites that nominally still exist but are shadows of their former selves (Slashdot, Tumblr post-porn removal, Digg).

I suspect Reddit management is making a classic mistake and operating with a linear model of their options when in fact the situation is very non-linear because of the fact that goodwill feeds back on goodwill. It's only locally linear and they can leave the linear domain quickly and irreversibly.

To what end? The only thing it accomplishes is making them look petty.

Well the moderators could just strike in protest? Which would probably cause more issues

It would look even worse on their part, and there will probably still be a lot of people boycotting Reddit by their own volition regardless of how the site operates.

because they depend on free labors of people that are going dark for their business to function

I think Reddit will actually still run for quite a while without moderators as most egregious spam is caught by auto moderator rules (although set up by moderators).

I moderate a few subs and rarely do things manually.

So short term strikes won’t have much impact other than degraded quality.

Also, there’s already a process for “abandoned” subs where if subs aren’t moderated users can request mod access. So if mods go on strike, new users could request mod access.

For some of the larger subs I think this would actually be healthy as there are lots of subs with toxic mods but there is no way to oust them unless they choose to leave.

And then lose the moderators that make each sub Reddit work, they could do that, but then it would just turn into Voat eventually.