My camera's sensor captures 33 million pixels (max. matrix of 7008x4672). To view that image on my 5120x2160 pixel monitor, the computer uses some kind of downsampling software. Similarly, print drivers (including Qimage) must also downsample to arrive at Epson's print head max of 720 DPI*.
That depends. Your 7008x4672 camera is good for 9.73x6.48 inches at 720 PPI so anything smaller than about 9.7x6.5 inches and it'll downsample. Bigger than 9.7x6.5 inches and it'll upsample to 720.
* How can Epson then advertise a "max print resolution" of 5760x1440 DPI for the ET-8550? What do they mean?
You are overcomplicating things by trying to make some association between 'DPI" and "PPI". A "dot" is not a "pixel". Just because your printer can spit 5760x1440 "dots" on a page doesn't mean you can equate each one of those dots to a pixel. A dot can only be one of a few primary colors: to get a full color equivalent of a "pixel", you'd have to mix multiple "dots" together to get every color you can reproduce in a "pixel".
So Epson would never try to claim that their printer can reproduce an image at 5760x1440: they use a lower multiple (usually 720) and their drivers run at that PPI. By the time the printer mixes 16 dots (8x2) made up of colors like cyan, yellow, magenta, red, green, blue, black, and gray, you can get a reasonable faximile of about 720 PPI of "image". Similar with Canon: they wouldn't claim Canon printers that run at 4800x2400 can print an "image" at that resolution. By the time you muddle together all the "dots" you need to get a full color image, we'll say you have about 600 PPI worth of "information" available on the page.
BTW, your camera even does something similar since among your 7008x4672 pixel image, your camera only captures one color (red, green, OR blue) for each of those pixels. So it is only capturing 1/3 of the color information and the other 2/3 is "guessed" based on neighboring locations. So you can get pretty complicated (convoluted) trying to define what an actual "dot" or "pixel" really is. The bottom line is that most Epson drivers run at 720 PPI and most Canon drivers run at 600 PPI. DPI is just a sales figure to tell you the absolute limit of the hardware (printhead, drive, etc.). If you like cars, DPI is more akin to horsepower and PPI is like 1/4 mile time since DPI is the output of the "engine" and PPI is more like what results end up on the paper.
Mike