Definitely very important for me. ^_^
But as long as we could customise the modifier, it's no problem.

@Stéphanie, no, on Windows you have to create a virtual desktop first with Ctrl+Win+D, and to use Ctrl+Win+arrows to switch between these. Windows use the Win key for almost all OS-related shenanigans.
But sure it’s a valid observation. These can be altered, of course, in Mac’s Preferences > Keyboard > Shortcuts > Mission Control... but I assume Mac’s keys are more important for Macs’ users.
Anyway, these nudge keys should be customizable too.

(just beware that on Mac, Cmd+ left or right Arrow is used for changing Desktops, I don't know about Windows)

As we have the option to multiply increments by 10 with Shift + arrows (or Shirt + click, etc.), it would be nice to also have another shortcut/key to divide them by 10.

In Indesign you can hold down keys to make TINY TINY moves, almost pixel sized moves, then larger moves with the single press of the left and right, and then even larger moves while holding shift.

I work in print production and work with a lot of product placement, aligning and shifting things to make sure they have even spacing and not all of these product items are in layer masks. Lately I noticed there's a HUGE shift in how things move in Adobe Illustrator and I believe it's created more work to where I have to zoom in to adjust and even when I hold shift and drag it doesn't move.

Check out the Astute Graphics plugins, specifically "DirectPrefs." I believe that one is free. It allows you to change the increment for nudging.

With Shift, we can multiply the Cursor Key Distance by 10. Please add a modifier to divide the CKD by 10.

I would like a keyboard shortcut like the Shift+Ctrl+Arrow combination in InDesign that allows very fine grain object movement. Actually, this would be great to have in Photoshop as well.

Corel:

Shift + Arrow does ×10 nudge, leave it as it is.
Alt + Arrow is reserved for 'nudge with a copy', don’t touch it (and it takes away Alt completely)
So we have Ctrl+Arrow and Ctrl+Shift+Arrow left: first one is ideal to have 1/10 of the increment value, and the second could be even 1/100.

While an object or text block is selected, holding ctrl/cmd and pressing arrow keys to nudge doesn't seem to have any effect. Could this not be used to nudge by a small increment?

When you are changing the value of a number within illustrator, the up and down arrows + ctrl/cmd make the number change by a 10th. Could the same not be used for moving an object or text around, maybe a 10th of the set "keyboard increment" to make smaller nudges? It could even be set in the preferences menu how much the ctrl/cmd + nudge increment is.