Is it a good idea to require members of the community who want to see a new topic area to participate a certain amount in that area? Is there any hard data indicating the quality (as measured by community approval, or any other metric) of posts from posters trying to meet a quota vs those from posters who are participating without any requirement to do so?
Any hard data? I don't believe so.
However, in my experience, any type of interaction quota is bad simply because it more than always leads to poor quality interactions. That's because it's not just about generating a natural interaction, it's also about meeting a quota too.
One good example would be something you may find in Stack Exchange communities. Sometimes users who join a new stack exchange may feel they need to get their reputation up. In order to do that, they have to start interacting with the site, especially on community submitted questions.
Due to that, they may try to answer anything, including questions they may not have the best answers for as opposed to answering questions that are within their field of knowledge.
The same degrade also happens when post counts and other post count achievements have existed in communities. Users will often post one line sentences in order to boost their post counts and try to get the top poster in a community. Although it's not a quota, the achievement is driving their activity, which leads to poor interactions.
Therefore, setting a requirement to post may not be a good idea under any circumstance. If the topic of discussion is vast enough to justify a new topic area, then the topic area should thrive naturally. If it doesn't, then you should not force it for the sake of quality. As quality is pretty important in most communities, I would strongly not recommend the approach of quotas.