It has pretty much always been assumed by a lot of people, including myself, that rendering engines are colourspaces agnostic, and whatever your primaries are, it should not make any differences.
An interesting thread with some VFX industry veterans about the Academy Color Encoding System has been ignited by Steve Agland.
He was describing issues while rendering in ACES RGB colourspace where the rendering equation could generate some very saturated colours, colour clipping and loss of details. Since we have started this notebook, Steve has written a post illustrating those issues, I suggest that you take a look at his notebook.
As we were discussing, Zap 'Master' Anderson pointed that he was assuming primaries wouldn't matter but that it was wrong.
The TL;DR; version of Rick Sayre from Pixar
The RGB basis vectors typically become non-orthogonal when transformed to XYZ, and definitely so in this case.
Thus there should be no surprise that component-wise multiply does not yield a proper transform between two non-orthogonal spaces.