All or Nothing - Cleanup and Overhaul
To allow 3rd Party Plugins it would need to be an all or nothing effort, otherwise it could be too confusing for new users which, once word gets out, will be a pretty big amount. If decided to re-allow 3rd Party Plugins we need to first start a process of going back to closed plugin questions ( unfortunately, sorry! ) and filter out which ones are considered to be on-topic / good quality and still close the bad quality plugin questions. This will give a basis for new questions to come ( people love pointing to the sidebar and say "This is on topic, why isn't mine!?" ), which is quite an overhaul and possibly easier than first thought since we're looking for question quality. It would also need a little commitment from the community to work. That's phase 1.
Phase 2 would be to completely redo and reword the help-section and report options so that it's very clear and concise what is considered a good question, a bad question, on-topic, and off-topic. People may not look at the help section initially but many people love using it in the comment section to point OP in a direction that will help them format their questions in the future.
By opening the floodgates there's going to be dam building of "close-question" reports and much more, as Goosen pointed out, there doesn't seem to be a great many of 3k users contributing so it may be beneficial to create a topic and see if we can create an "A-Team" of 'user-mods' - people that stay on-top of the review stack. Of course none of which would be obligated but this would be helpful at the start of the flood.
Next would have to be tags. We should allow all plugins, no bias except plugins 2 years or older. If the author isn't keeping their plugin up-to-date then we shouldn't have to support it, at that point it's legacy. If a plugin author doesn't want their plugin to be answered here ( Plugin Author makes revenue through Premium Support ) they will unfortunately have no choice but to Opt-Out via a WPSE-Meta topic, at which point we can use if a users asks a question on the topic and wonders why it's closed. Depending on how many plugins actually do this, it could be just as a nuisance as the Opt-In system that @kaiser suggested but I feel there would be less plugins out there that would actually do this.
Finally, if possible to automatically add a generic plugin tag whenever a question is tagged with plugin-{$slug} would help users filter out all plugin questions if they decide to. If that's not possible it may be difficult to keep plugins from people feeds since there's too many to filter out one by one.
I don't think there's going to be any one idea that's going to be the be-all end-all solution, all we can do is try to make things as clear as possible on what's on-topic and what's not to keep out the poor questions.
TL;DR
Reformat old plugin questions as a base, build upon it with the Help section, create the A-Team of user-mods, don't support old plugins and allow plugins to manually opt-out via WPSE.Meta, add generic plugin tag automatically.