Just for information:
The Riviera procedure is not used to protect the rich "Cap d'Antibes" but to protect the middle class downtown.
In fact, the Riviera produces a higher noise level along the "rich" area than the ILS.
A "classic" reason for the ATC (at least in Nice) to ask an acft to "expedite T/O" would be that... it just takes to long!
It never stops surprising new atcos, coming from bigger airport (CDG or ORY), to see that what goes smoothly in Paris, always seems to take close to eternity in Nice. When we ask, prior to the T/O clearance, if an acft is "ready for T/O", and the answer is "Yes", then we expect the guy in the cockpit to release the breaks within a few secs of the clearance, not 1 minute latter (I know that sound stupid, but...)!
If we wait 1 min, then ask to "expedite", chances are the message will be sent when (or just afer) the T/O run starts.
Like Eva San just said, we just append to have some limitations (mountains, cities, rich peoples... being french), and are trying to do our best.