Canon tried with some Bubblejet printers, like BJC4300. It needed three passes per line (R,G,B) slow and lower quality.
I think also it was expensive, since I wanted to get it, but failed to find it.
OTOH, a 10 year old HP multifunction can scan things at 600DPI in acceptable quality and detail, in a very reasonable amount of time.
If you want to go compact, but fast, there's Kodak Alaris' "i" series scanners which can scan both sides at the same time. Scan time is ~4 seconds per double sided A5 page at 600DPI, and less than a second for ~200 DPI.
Interesting. The drawbacks you describe seem to be limitations of the sensor and image processing technology available almost 30 years ago.
For example, my Epson inkjet printer can do about 10ppm at it's lowest print quality, so it can mechanically move and scan a page against the printhead every 6 seconds; a 1Mpx sensor with a 60Hz frame rate will generate 360Mpx in 6 seconds. Even if you throw away 50% of the data (overlap areas, next page load, motion or optical blur at the edges etc.), that's still enough data for a ~1400 dpi raw resolution of an A4 page at the fastest speed. If you are willing to go slower, the resolutions the system could achieve seem outside the range of any flatbed.
Of course, you would need e very beefy image processor to handle the multiple Gbps raw video data and process in real time down to the final scan image, but the actual corrections seem very achievable with modern algorithms.
Outside of the cost of the image processor, another showstopper I can see is motion blur on the sensor, stopping the heavy printhead from its inertia, so that you can have a still image, will kill your total scan speed. But perhaps you can just pulse the LED, or a gas discharge lamp, and impress the sensor with near instantaneous flashes of light.
I had a Canon scan cartridge around 1999. It was slow, but worse, it was very finicky about the printer cable being used - which at the time could be very expensive and were not included.
It worked, but there was a clear linear pattern across scans. It worked for some things, but wasn’t the best for photos.
I have an HP All In One and I was quite disappointed when I first used it to digitize photos. It's nowhere near 600DPI. The quality I got from the scanner was worse than taking a picture with my phone!
Of course taking a picture with the phone requires good lighting and the photos you want to scan need to be flat.
I think also it was expensive, since I wanted to get it, but failed to find it.
OTOH, a 10 year old HP multifunction can scan things at 600DPI in acceptable quality and detail, in a very reasonable amount of time.
If you want to go compact, but fast, there's Kodak Alaris' "i" series scanners which can scan both sides at the same time. Scan time is ~4 seconds per double sided A5 page at 600DPI, and less than a second for ~200 DPI.
That thing zips, but is not cheap.