Reddit can remove the mods of any sub at any time and simply open the subs back up. They are allowing them to remain shut now as a PR move because it's a worse look if they take them back by force. But make no mistake - that's what will happen in the long run.
The thing that is really going to hurt Reddit in the long run is that all of the Reddit links on Google are "breaking" - if someone searches something and a Reddit post comes up as a result, there is about a 7/10 chance that the sub is private and the post isn't visible. This will hurt Reddit badly in the long run because Google will remove these results if they stay that way for, say 2 - 3 weeks. Then Reddit loses the ad revenue and new user capture they were getting from organic Google traffic. They can't simply get that back by reopening the subs, either - once those pages are downranked on Google, it will be difficult for them to rebuild the traction to get a high listing. Some have been there for 10+ years.