I have often heard the claim that the Apple /// was intentionally crippled, usually for marketing reasons and always with the implication that it did not have to be done. But is there anything to substantiate that?

Here's my thoughts:

The original Apple II had a rather quirky design. Sometimes that was due to technical limitations, such as the tiny memory windows to Apple Bus cards. Sometimes that was to simplify the hardware design, such as the non-linear mapping of the video frame buffer. Software developers often compounded the problem, by depending upon the hardware and firmware's implementation rather than using higher level abstractions. (Not that the had much of a choice, since that abstraction was limited and performance was always a consideration.)

On top of that, the design experience within Apple would have been quite limited. Indeed, design experience would have been limited in the PC industry as a whole. Backwards compatibility was not really a factor in an industry that had a plurality of incompatible vendors, and vendors that were barely compatible within their own product-lines. The PC had yet to learn the lesson of the mainframe (in the business or technical context). So it may have made more sense to have mode splitting.