I was looking into greater staff of healing for my Cleric, but looking into it, it seems kinda awful.
The concept of not having to prepare things like Restoration or Remove Disease, but since they’re in the staff as 2nd and 3rd level spells means doesn’t seem likely would be able to counteract very much at 8th or 9th level.
I suppose the 3rd, but almost certainly not the 2nds…
Remove Disease would have this problem, yes. If you are meaning 8th level diseases that you are facing, you are also correct that the 3rd level spells would still be effective - you would need to get a success on your check. But the 2nd level versions would need a critical success to counteract an 8th level disease since it would have a counteract level of 4.
You could also still use the staff's spells effectively against lower level diseases if you or your allies happen to become afflicted by them.
Restoration doesn't use counteract checks though. It should be useful even at the lower spell levels.