The reason it seems more off-topic/spam posts than the per-site Meta's is because it is the only meta site without a reputation barrier (despite the listed "participate in meta" privilege [see https://meta.stackexchange.com/questions/254054/remove-meta-privilege-for-mse-only for the reasoning]).
Anyone can ask a question here and it doesn't even require an existing account on another SE site. Yes, this means it can lead to some spam and off-topic questions, but there are a number of benefits:
- It gives a voice to low rep users who cannot participate in their own site's child meta. While the question will probably get closed since it only pertains to a specific site, they usually will get feedback via comments and answers before that happens.
- Bug reports/feedback from users without accounts
Echoing what I said in my comment, if you turn MSE into a "High Rep Members Only" club, you only further isolate low reputation users from contributing to improving the Stack Exchange sites.
As for the Spam/Off-topic questions - how long does it usually last? There is more than enough activity on the site to get spam nuked within minutes, and usually the off-topic questions get closed pretty quickly, and deleted not to long after that. If this wasn't happening quickly enough, it would be worth considering other options, but since we are not overrun with these types of posts, this seems to be unnecessary.