Yes, and the ones of the objects support drivers too.
What is the interest of letting them support animation and drivers but not the eye icons?
I try to find a workaround to link the visibility of some objects and it is frustrating to get stuck because of this restriction:
https://pasteall.org/blend/0dc2596a55d7412780487cc2d96f2fbe
Linking automatically the eye and screen icons in both ways could do the job too.