I don't honestly think having weather on the ATCOs primary radar display would help that much - there is such a disparity between different airlines etc about what severity of weather needs to be avoided etc, that second guessing a pilots decision would, to my mind, cause a greater overall workrate.
In the LTMA, where it is very densely packed traffic with a multitude of crossing tracks, we put a flow rate on if weather avoiding is taking place; everything becomes non standard anyways, I'd rather we managed the situation as it comes, rather than trying to be smart and outguess the aircrew.
Even if we had weather radar capability on each console, we would still need to introduce MDIs etc - therefore it would not save much in the way of workrate.
There is often the instance of pilots from the same company taking different courses of action - some will fly through certain cells, whilst a minute earlier, a colleague has requested avoiding headings. Either way, you can't win!!