As I understand, the downlinked info comes from the MCP, but I might be wrong.
The MCP is always controlling, and the FMS cruising altitude, or enroute restrictions would not guarantee you, as a controller, much.
After reading back an ALT clearance, pilots usually set the new alt in the Mode Control Panel, initiate a mode to climb or descent, usual Level Change, (or Flight Level Change in Airbus), or a Vertical Speed ( for small ALT changes), then update-if needed-the FMC.
The FMC(G) is not the primary toy for complying with altitude changes.
It also would not speed up the actions of the airplane, and that is probably what you as ATC is looking for.
Hope this helps.