I studied the MS antitrust case extensively when it was happening, and I agree that the abuse against BeOS was MS greatest antitrust offense. However, as a fan of BeOS, I see no evidence at all that Be Inc. would have been successful if MS hadn't abused its position. Unfortunately we will never really know what might have been.
Yeah, Be Inc. made no sense at all for its own purposes. The reason it existed is that Apple (yes, that one) had fired one of its executives - Jean-Louis Gassée often abbreviated to "JLG" - and he wanted to show they were wrong.
AIUI the intended exit was either an acquihire (Apple gets JLG back and the Be Inc. "journey" ends once people tidy up) or maybe Apple's software side fully embraces Be Inc. (after all JLG is sure he's correct about what Apple should do) and absorbs the entire entity as Be's operating system BeOS becomes the new Apple OS.
That part isn't crazy, it's the early 1990s, affordable CPUs have virtual memory support, the physical size limit is looming, software reliability is worsening, Apple's 1980s co-operative multi-tasking operating system is not up to the job. If you understand the big picture it's obvious that you want something closer in principle to a Unix. You could hire somebody to build one (as Microsoft had for "Windows NT") or some people might build one in their bedrooms (Linux) or you could buy one which already exists, so, that's what Be Inc. set out to be.
In the end Apple decided that if they're going to re-hire an executive who they have fired previously it should be Steve Jobs. The moment they've made that decision, Be Inc. was superfluous -- JLG knows Steve isn't going to hire him, Steve hates him, so next the priority now is to help the money get out so that investors will continue talking to JLG. Fortunately the Dot Com bubble happened, Be floated on typical bubble era nonsense, about how their system is somehow perfect for the Internet, and that was enough for the big money to get out, leaving the wreck for the poor Be fans who were still buying even after the last dregs were gone.