When there is a large number of comments, why not arrange them as pages instead of moving them to chat area? At the bottom of the comment area, just leave a sequence of numbers from 1 to the last page to navigate through the comments.
First off, a general comment: this site (Physics Meta Stack Exchange) is for discussing the policies and community of the Physics Stack Exchange site. The policies and moderation on this site are, for the most part, run by the community, and this is where we discuss those aspects.
The site is hosted by Stack Exchange (the company, which also goes by the legal name Stack Overflow), and it runs on software designed and maintained by Stack Exchange, like the rest of the network. The main place to discuss this software is Meta Stack Exchange, the network-wide meta.
If you post feature requests for the software here, then we will probably be able to point you in the right direction. But for feature requests to be implemented by the SE development team they need a lot of community support, and the main meta is a much better place to get this than here.
That said, regarding your suggestion: it's just not going to happen. As noted in the Help Center, comments are transient and ephemeral, and they're not designed to contain long-lived discussions.
This has been the overwhelming design philosophy used by the SE developers when designing the systems that interact with comments for more than a decade, and it's not going to change any time soon.