Be definitely wasted a lot of time in strategic churn, porting from Hobbit to PowerPC, BeBox to Mac, PowerPC to x86, PCs to thin clients, etc. For the brief time that BeOS ran on Macs, the likely goal was not to get Mac users to switch to BeOS but to convince Apple to buy Be. I heard that Apple offered $75M for Be and JLG refused. (Some people assume that Apple offered the same amount for Be and NeXT, but that's pretty unlikely considering the difference in maturity.)

BTW, where you wrote Rhapsody you meant Copland. NeXTSTEP was renamed to Rhapsody (and then OS X) after Apple bought it.