This actually has a relatively long tradition. Wallace Berman was famous in the 1960s for his copier art, he discovered you could put the copier on its side and it had a relatively high depth of field. His late '60s copier artworks are icons of the LA art scene, and are highly collectible but alas, are doomed to deteriorate due to the impermanent copier media.
I played around with copier art in the early 1970s when I was in art school, mostly because everyone was interested in it but nobody really did it. I found the 3M VQC copier series had some amazing properties, it was designed for reproducing photos and had much better continuous tone reproduction compared to regular xerography. It was like gravure printing, and had an additional bonus that the paper was perfect for silverpoint drawing. But alas, the VQC copier was too expensive for commercial use and eventually was discontinued. But oh was it a sweet copier system.
So there's a lot of history of flat copier art that turned into scanner art. Computer Arts magazine did a feature a month or two ago about "scanography" by some designer that sliced fruits and scanned the cut sections flat against the glass. This is a fairly common technique now, so it's hard to think of how powerful these images were, way back in the 60s when copiers were first invented.

Hmmm. Maybe my scanner just sucked, but I never got good
results when I tried this sort of stuff. Nowadays I don't
have a scanner, so I can't try it again.

Results will depend on your scanner, Eli. Some scanner sensors have good depth of field, some don't. Some do 3-pass scanning, some do 1-pass (better). At most, you'll have about an inch off the scanner plate that you can resolve.

It doesn't appear that this is still active--but I hope someone receives this. I've been scanning flowers for a couple years. It evolved from scanning at a low dpi for T-shirts. I accidentally discovered this open-lid technique--by forgetting to close the lid one time. ANyway, I'm running into some issues lately with the connecting ribbon on the bottom of the scanner casting a shadow, getting a greenish background, when I put a black box I don't get the nice shadows and get distortion on the sides from the box. I'm scanning at 300 dpi and saving as TIFF or JPEG. I could use some input. Anyone out there have some suggestions? Thanks. Denise in Chicago's south suburbs