I just finished 'testing' my new Canon Pixma Pro 100. I took a full Canon 5D4 image, resized it in PS CS4, and printed the entire, non-cropped image through the Lightroom print dialog onto several 3" x 5" sheets of Epson Premium Semi Gloss paper. (Not that it matters to this test, but I profiled/calibrated the printer using an i1 spectro and included software). I found that extremely fine details in the image printed smaller and clearer at 1,200 PPI than at 600 PPI, but were slightly less clear at 2240 PPI (6720 pixels into 3").
These results are the result of LR and/or the Canon print software massaging the image data before spraying ink droplets.
I then repeated a test I did on either an Epson 1280 or R1800, I don't recall, from many years ago.
I created an image consisting of a vertical, a horizontal, and a 45 degree single-pixel line, in each of CMYK and RGB fully-saturated colors. Abut each of these characters at the lower left corner to get an idea: |/_ .
I created these images at 300 PPI, 600 PPI, ans 1200 PPI. When printed, the 600 PPI lines were half the thickness of the 300 PPI lines, but the same saturation. The image at 1200 PPI had lines about 2/3 the thickness of the 600 PPI lines, and around half the saturation. (The printer cannot print at 1200 PPI, but does a fair job trying too). I then downsampled the 1200 PPI image to 600 PPI using CS4, and Bicubic Sharper. Surprisingly, this restored the color saturation while only slightly increasing the thickness of each single-pixel line from the size it was at 1200 PPI.
I achieved similar results with the Epson printer, long ago...
IOW, these inkjet printers can resolve solid, saturated details at far smaller physical sizes than most photograpers can imagine.
I also didn't see any reason to upsample an image to get sharper details. This might change if you are printing at less than 300 PPI.
As an aside, this new Canon shades yellow tree leaves without visible black in droplets. The same print, from the Epson R1800, has naked-eye visible black droplets in the same leaves. I don't know if this is due to smaller dye droplets from the Canon, vs the pigment droplets from the Epson, or some other technique... Both printers were profiled/calibrated on the specific paper used.