I think that's too strong of a solution to the problem; it's punishing the 99% well-meaning low-rep users for the actions of one or a few idiots. I've always liked the idea that despite the 20-rep barrier on talking, a new user can at least jump into one or more rooms, "listen in" if you will, start being part of it and maybe see that as an incentive to start participating on the site. Maybe I'm over-romanticizing this, but there's a reason that when you enter the room, you see yourself flying into the user list.
Regarding your second idea, that's interesting. Although maybe it shouldn't be a setting, but happen automatically once a room crosses a certain activity threshold. The question remains, should users also be considered to be leaving once they haven't talked for a while?
As an aside that only tangentially targets your request, but is in a good place here to make people aware of what's happening:
To address this and many other issues and requests, I'm currently working on extending the chat permission systems in order to make three things possible that currently aren't (with the single exception of suspensions):
Subtractive permission adjustments. As I said here, the current permission system only allows you to give users additional permissions, never remove permissions from the default set.
Temporary permission adjustments. This will, for example make it possible to give users time-limited permission to chat despite low reputation, or ban a user from a single room temporarily.
Global permission adjustments. The current system only allows adjusting a user's permissions for particular rooms, not globally. Global permission adjustments will, for example, make it possible to prevent a user that usually behaves, but abuses the flagging system, from flagging at all, or to give additional site-wide powers to certain users that have shown to be a great help, but aren't technically moderators.
These are just examples; I'm not promising that any particular one of them will actually end up being implemented (though at least some probably will). Currently it's just about making such a thing even technically possible.
This permission system revamping is at an early stage, but somewhat functional already (although only developers can currently make permission adjustments). One of the example adjustments that I've added (for testing; it may or may not eventually exist in its current implementation) is a kickban functionality that prevents a user from re-entering a room (and thus having their avatar displayed). For what it's worth, today's troll was a good case to try this out, and once I started doing that, it seems to have made them give up pretty quickly.
Once all of this is stable, we can start creating fairly fine-grained permissions and restrictions that can, even temporarily, be applied to users, and because it can be fine-grained and temporary, we can even consider giving the power of applying these adjustments to normal users, taking some burden from the moderators (or at least giving them time to respond).