Pigmented inks are a suspension, and do settle and coagulate with time. The coagulation of pigments is what can clog the print head. Even with vigorous shaking, they are difficult if not impossible to re-suspend well. Canon, Epson and HP do have additives in the ink to keep them suspended, and tend to work quite well
there’s a big difference between settling and coagulating. I’ve never seen any evidence of suspended particles in epson inks coagulating (sticking together in big clumps). I know there was an extensive thread a few years ago about ink settling out, but the main point in that thread was trying to use a centrifuge to simulate what would happen over time, and at the time I didn’t feel that approach was valid (and still don’t).
I haven’t been agitating my Epson cartridges for several years now. Every couple of months I print Bill Atkinson test page and compare it to the original page I printed when I installed the printer, and I have seen no color drift in this machine in 3 years now. Some of my inks I go through pretty quickly, but others may be in the printer a year or more. I do use different size cartridges in the printer based on how fast colors are used (blacks are all 700, orange and green are 150 ml, all the others are 350ml. ). This avoid excessive length of time for any one color.
There is some agitation of the inks as the printer prints. There is also some agitation due to the pressurizing and collapsing of the bag that contains the ink each time the printer does this (which is more often than just when it is shut down). The suspensions are designed to be easily maintained.
As far as vigorous shaking, I would caution against that, and do feel it is unnecessary. When I buy a new cartridge I gently agitate with it laying flat, rotating it constantly for several minutes. Of course I also don’t buy expired inks so I have less concern than others, but there are plenty of epson users that have done very well (such as Dan) which indicates coagulation isn’t a problem.