Worrying about what the weather at your alternate is doing is probably not that high on the controllers priority list as he deals with the deteriorating traffic situation at your destination.
That is a good point. Inbound to Sydney with a thunderstorm passing through the controllers sound like they are working at maximum capacity just to stack everyone up and give them an estimate of onwards clearance time. To expect them to be monitoring diversion port weather trends at the same time is unrealistic in my view. That's from a line driver, any controllers care to comment?