Illustrator is not the best choice for printing a CMYK image on an inkjet because Illustrator is optimized for Postscript printing, color management is best handled in RGB.
If the application offers a choice of Absolute Colorimetric intent along with a "Let [application] determine colors" workflow, I expect it to produce results according to that intent.
Incidentally, the "Let Postscript® printer determine colors" option is grayed out in Illustrator when printing directly to an inkjet via the driver, without a dedicated RIP.
Preserve Numbers (Ignore Linked Profiles) option is available in Illustrator for CMYK.
Only when printing to a CMYK device (like a laser printer or a RIP for an inkjet). In my case (printing directly to the inkjet via the Epson driver) the "Preserve..." option is grayed out and not selectable. So, its usefulness in this case in out of the question.
In general, Illustrator is not the best choice for printing a CMYK image on an RGB device. InDesign, on the other hand gives you the option to override this color management policy.
Right now, I'm not interested in which application or workflow is best for printing or proofing a CMYK file. I know the answer to that already, and it was not what I was asking.
What interests me is that the Absolute Colorimetric intent is not producing the intended results in Illustrator, though the selectable option is there.
So, the question still remains: is this an impossibility in Illustrator? If it is, so be it. If it isn't, which workaround will make it behave properly?
By the way, I have 25 years of experience in digital workflows, and I am a veteran production specialist. I am definitely not a beginner.
Routinely, I use a RIP to print color proofs to an inkjet. This particular use of Illustrator which I describe here is highly unusual for me. All the more so, I want to get to the bottom of what I still consider a misbehavior, no matter how "advisable" or not it is to use Illustrator in this fashion.