Shouldn't you be able to drop the staff after you complete the SI MQ? Or even deactivate it etc. would certainly make sense.

Yep, you should probably be. Once again, game mechanics.

Sense? Do you remember who it belongs to?

Heh, now there's a point I forgot to take into account. However depending on the views (how much of a Sheogorath you are) it's next to impossible that you couldn't. There's only one other artifact which comes close (the scourge) but even that one probably would have no effect on it's maker (remember, it's the "blood" and all that).

If you believe you really are Sheogorath now, why would you want to break your own artifact?
And if you believe you're his successor rather than the real deal, then you simply don't know how to do.

You hold the title and own the symbols of office, but you're still not a daedra. You don't have the power to reshape the world or even simply teleport people to Execution Point (it would make those "defend the realm" deal so much easier).

Well.. since I added MadGod powers I do But the thing is they changed the shrine quest so nicely, I think it's odd that there's NO change in the everscamp quest. Not even a different journal entry (a snicker perhaps? funny remark.. something ). + who do you think made the dogs rain huh? (yes, you could say haskill, but then why are you needed? )

Sheogorath is a god. He can do anything within his own realm. I think the player becomes Sheogorath; how could one possibly defeat a Daedric Prince in battle unless one is a Prince as well? Or an Aedra. Or someone who has CHIM. But anyway....

Bethesda could not possibly give the player all of Sheogorath's powers. His powers are only limited by his imagination (which is probably far more flexable than human imaginations.) And Bethesda didn't seem to worry about continuity between the Shivering Isles and the original game (try using the Staff of Sheogorath during the Battle for Bruma. I'm sure they didn't intend that.)

The reason the player can't drop the Staff of Everscamp as Madgod is because the developers didn't think of that. Simple.