What are the advantages of this 4000 ppi?
Sorry, but your unit is not the right one : PPI means
Pixels Per Inch, and pixels are for pictures! (pixel = picture element)
But an imagesetter or a printer
(laser or ink-jet) prints
dots (not pixels!), and then the correct unit for the resolution of a printing device is
DPI (Dots Per Inch).
********
20 years ago, raising the resolution above 2400 dpi had the advantage to get the 256 levels at screen frequencies higher than 150 lpi: 4000 dpi should have allow to print up to a 250 lpi screen with 256 levels...
Today and since the beginning of the 90's, the SuperCells screening technology allows to get the 256 levels of a 250 lpi screen with only 3000 dpi or less.
(read
Gordo's
blog for more explanations on SuperCells).
But even with SuperCells screening there is still a limit to the highest screen frequency that can be outputted with a given resolution, and having an higher resolution still allows higher screen frequencies...
(for example, my imagesetter outputs screens up to 200 lpi at 2400 dpi, and needs it's 3600 dpi highest resolution for higher screen frequencies, up to 425 lpi...
... but who can print a 425 lpi screen with an offset press??? )