8 good bits per channel is all a printer needs. Editing existing 8-bit to a degree can introduced banding.
digitaldog.net/files/TheHighBitdepthDebate.pdf
A good read. Altho tech has progressed (and maybe regressed lol), all the bit-depth fundamentals remain sound.
Continuing from that article's conclusion, and for the OP, for me it's an easy decision: anytime I'm offered a choice in my devices/apps to discard some data, I say no. In my use there's rarely any meaningful benefit or "economy" to discarding data, while the risk of encountering issues goes up. Plus tech advances can reveal the shortcomings of past decisions when returning to earlier works.
So like many things, bit depth was one of those "set-it-and-forget-it" choices I applied to my workflow years ago and haven't thought too much about it since. This thread is a nice reminder though to check these things once in a while..., especially after software updates etc to verify things are still set as we want them.
So I don't downsample before sending files to my HP Z3100/3200 printers. HP says the print driver downsamples to 8 bits per channel, so I've preserved the most data in my files until that conversion is necessary. (Ok technically I can submit 16-bit images to the printer by bypassing the driver, but the printer firmware will still downsample to 8 bits anyway..., tho curiously HP suggests that firmware conversion can be better than the print driver's conversion, a diminishing returns rabbit hole I've never bothered going down...)
Speaking of printers tho, what's the story with more recent printers? (Mine are 20-yr old tech.) Do any of them process in higher bit depths now and give meaningful advantage from it?