My notions are that scanning as 48 bits won't hurt the result, but it will waste time and effort and storage space. Arguably might help slides, but it won't help prints. Print paper does not have it to give.

A printed magazine image has a dynamic range well less than 2.0, maybe about half of that (1.7). The blackest ink still reflects some light, the white paper is not all that bright, and the difference is relatively small. Photographic color prints have a dynamic range of maybe 1.8, certainly not exceeding 2.0, for same reason, even if a bit brighter paper. Film negatives might have a range up near 2.8 (but we don't view negatives). Slides can be greater, extremes perhaps up towards 3.5, so dynamic range becomes important, but not likely even near 4.0. These are not precise numbers.

Scanners and cameras do have typically at least 12 bits today (36 bits), because the extreme shift of adding gamma needs it. And this does help when scanning slides. But prints really don't need 16 bit output. Yes, 16 bits might help preserve radical correction shifts, maybe possible in slides, but not likely in prints (prints have already been corrected once, they don't need that much work).

We don't have opportunity to see 16 bits, our monitors and printers are 8 bits. All JPG files are 8 bits too (meaning 24 bit color).

If you might print double size copies, the 600 dpi might help (some, but the color prints really don't have that much detail to give either). Even copies of color prints scanned at 600 dpi and printed double size at 300 dpi will be visibily degraded some (but 600 dpi is a good try for double size). Grayscale might have slightly more detail than color (especially old contact prints). If printing original size copies, 300 dpi is plenty. No way to use more if printing original size. If not printing copies, video monitors are not large enough to even need 300 dpi (but an archive surely should be 300 dpi, for unknown future printing). If making Ken Burns style movies, then 300 dpi could allow zooming on small areas.

You say you have thousands of prints to scan, which is a big job, suggesting that before starting, the work deserves your spending a bit of time experimenting briefly with the various methods considered, at least scanning a few prints the different ways, to see if the methods actually do help your results. This testing should include actually printing a few of the scanned copies, to examine that result too, it's an important part of the process. You should believe those results that you can see yourself, meaning you ought to be able to actually detect and see that which you claim helps.