ATC do precisely that.
In areas subject to large numbers of convective storms (called by some controllers 'popcorn thundershowers') Flow management may put significant limits on the number of aircraft allowed through the airspace. In areas where aircraft are confined to fixed air routes the flow managers will normally put on an extended 'Miles In Trail' limit to reduce the numbers of aircraft. Controllers in sectors that start becoming difficult to work will give the surrounding sectors a maximum number of aircraft they can accept in a time period - to reduce workload and make working the aircraft in their sector safer.
@Ian W, many thanks. Can I ask if you know how many Miles In Trail would be thought sensible in a popcorn-thunderstorm area that's likely to have a lot of traffic?
BTW, when I googled 'Miles in Trail', I was startled to see that your own post in this thread, from half an hour ago, was one of the top results. Google's ability to track us in real time could give the airlines a lesson.