Wouldn't the emperor figure that the Nevarine would drive the empire from Morrowind? What good does the Nevarine do to the Emperor's interests? Is he concerned about the false gods in Morrowind?

Uriel foresaw alot of things, especially in his visions. Maybe he saw this as the setting of Morrowind was one of the key things to Alduin's Prophecy, and had to do it

Or maybe he considered the Nerevarine a lesser threat compared to Dagoth Ur. God knows what went on in that man's head.

Also, last I checked, he never actually did, did he?

Well he saw the events of Oblivion before it happened

It has less to do with visions and more to do with good politicking. Uriel, after the Imperial Simulacrum, became a shrewd diplomat. He would've understood the political risks of a Nerevarine rising of his or her own accord to be greater than the risks of sending him or her there himself with a wink and a nudge. A free ride out of prison, with admittance to the prestigious order of the Blades -- what person wouldn't be grateful?

The Emperor knew, because of the Elder Scrolls, that this prophecy would come to light. He simply decided to insert himself in the picture early on to be able to flex a little political muscle when it did.