Example 1: I have an object with Array modifier, almost every option changed - it would be a horror to re-enter all values in another object. I hold Alt and drag this modifier from Cube.001 to Cube.002 - it gets duplicated.

Example 2: Three objects have different materials, but I want the same texture for them. If they already have some textures enabled, it should be possible to change channels in Outliner - up, down, like in a modifier stack.

Why do we need to spin an object, Undo, change values, spin, Undo...?

I propose another modifier stack (for smaller mess), in which I change Spin values in any time. That will allow me to make a small corrections in objects profile and to make the mesh more dense when I need it.
A possibility to select a spin center would be needed. That could be an object's center or [OB: ] field.

It isn't a huge waste of time just to click Apply.

I would expect the same thing for fractal subdivision and Screw.