That was never going to happen. The value proposition for DOS and Windows was that they were open to running anything and everything. Microsoft was the ocean, not the shark.

As for adding features to browsers, they all did that. Netscape tried to build its business on "looks better in Netscape", and Microsoft simply implemented support for Netscape features (much like it had implemented support for 1-2-3 and WordPerfect features in Office).

There was never any prospect of "a proprietary web owned by Microsoft". In the mid-90s, Microsoft did have plans for a web-like network as a sort of distributed OLE (Blackbird), but quickly went "all in" on the web. The closest was the use of ActiveX controls on the web, but other browser makers could have supported ActiveX if they had wanted to. (Firefox decided against.)

Otherwise, neither Firefox nor Chrome existed when the anti-trust case ended, and there has never been any prospect of Microsoft killing either. It was Netscape that featured in the anti-trust case, and Microsoft won the browser case 2-1 on appeal.