I was in elementary school during Copland and the NeXT acquisition and so I wasn't there, but based on everything that I've read, the reason for the long gap between the purchase of NeXT in December 1996 and the release of Mac OS X 10.0 in March 2001 had largely to do with the inclusion of the Carbon API.
The story goes as follows: after Copland was cancelled in 1996, Apple then pursued the idea of purchasing or licensing an operating system from another company and then building a new Mac operating system on top of it. Existing Mac programs running on then-current System 7.5 would run in emulation under what's called the "Blue Box," which would later be known as Classic Mode in Mac OS X. New programs would run under a then-undefined API called Yellow Box that ran natively on Apple's future operating system. The questions were: (1) what would be Yellow Box, and (2) what would be the native operating system? The choices were Windows NT, Solaris, BeOS, and OPENSTEP. BeOS and OPENSTEP ended up making it to the "final round." In the end, Apple bought NeXT, and work started on a project called Rhapsody, which was essentially OPENSTEP with a Mac OS 8-style theme. Yellow Box was the OpenStep Objective-C based API, which would later be renamed Cocoa in 1998. Rhapsody was supposed to be released sometime in 1999 if I recall correctly.
In the beginning, it was expected that Mac developers would port their software from the classic Mac API to Yellow Box. However, some developers balked at the prospect of porting their code to Yellow Box, most notably Microsoft and Adobe. Given the importance of products like Microsoft Office and Adobe Photoshop to the Mac platform, during WWDC 1998 Apple announced the Carbon API, which was similar to the classic Mac API but was designed to take advantage of features such as preemptive multitasking and protected memory. Also, Apple announced that both Carbon and Cocoa would be based on a common substrate of C functions, allowing "toll-free bridging" between the two APIs.
The addition of Carbon was a significant engineering effort that contributed to the delay of the release of Mac OS X. There may have been some other factors, such as designing the Aqua interface and incorporating the feedback received from users of the Mac OS X Public Beta, which was released in 2000.
In the meanwhile, Steve Jobs was able to buy time for Apple through the introduction of well-received, now legendary products such as the iMac and the iBook. By 2000 Apple got its mojo back, and the attention became less on when Apple would finally release Mac OS X and more on anticipating what type of products Apple would come out with next. Eventually Mac OS X 10.0 would get released in March 2001, just in time to compete against Windows XP, the first consumer version of Windows based on Windows NT as opposed to MS-DOS.