I need this feature as well. I just paid for and published a private member area that I later learned anyone can become a member of.
For squarespace: While I'm grateful for the release, being clear about these constraints would have been helpful, warranted even. A "member area" implies privacy or exclusivity, if it's not it's just another space. So I'd recommend prioritizing the product roadmap to address this immediately or rename the feature to "Subscription area".