Grandexp:
You have made some terrific points. The best way to keep a printer working well is to use it. Your high volume use probably prevents certain issues, at least as quickly as someone who infrequently uses their printer. Purging the Pigment Ink cartridge can be an effective measure to maintain performance. Some regularly drip fluid (solvent) onto their purge pads to prevent clogs of the purge system as well as the print head.
The algorithm I would use for diagnosing the OP's specific problem - completely missing Pigment Black ink nozzle check missing - can be divided into three major categories:
cartridge issue (ink starvation from either no ink or an impedement to flow of ink from the cartridge for which a purge may fix the issue),
print head issue (clog, bad electrical contacts, or electrical failure), and/or
purge system issue (clog, disconnected tubes, pump failure, etc).
The first thing to try is another cartridge, preferable a new OEM Canon cartridge because it presents the fewest variables, but any known working cartridge will do. One can, of course, purge and refill the same cartridge. If the new cartridge does not work then we move on to the purge system and the print head. Oftentimes, testing the purge system along with trying a new cartridge, as well as check/clean electrical contacts, is preferred since it's quick and easy to do and facilitates diagnosis.
Since the OP did try a different cartridge, it is less likely the cartridge was his problem. Still, from what I read, the OP did not state if it was a new cartridge, an OEM cartridge or even if it was a known working cartridge. So, we cannot be 100% sure the cartridge is not the problem.
In the third post on the thread the OP states he refills with Hobbycolors ink using the German/Durchstich method. Hobbycolors ink has cropped up as a Pigment Black ink in clogs. Ghwellsjr did some experimentation with various pigment black inks which are linked in the thread. I have also used Hobbicolors pigment black ink for about a year and had no clog issues. I switched back to Precision Colors IS pigment black because of highlighter smearing issues with the Hobbicolors long before ghwells conclusions. Maybe there is a bias suffered on the forum and it's thought Hobbicolors is the major culprit in clogs. Maybe not. A running tally of ink brands that have been involved in clogs may illuminate the issue further.
Most text print head clogging can be revived by soaking with Windex for 30 minutes to an hour. I did recover clogged print heads most of the time.
I wish most pigment ink print head clogs could be fixed with a 30 minute Windex soak, but it isn't so for the majority of users considering the experiences reported on the forum. Again, maybe it's a bias in that we only see people with stubborn clogs, but I doubt it. I wonder if you have such nice and speedy results because you have people closely monitoring for changes in print output which you then act upon quickly.