Hot weather places a tremendous load on the grid.
Cold load pickup can too. It's like starting a cold "old" car and 5 degree weather. What happens to us after say an ice storm, the equipment and everything are very very cold. Plus everyone is at home now so you are picking up more amps/load on that feeder than what was on it when it went out. We also have reclosers (best way to describe them would be to say a mini substation that looks like a transformer in a way) that can be tricked once you try to heat up the feeder it is picked up by the recloser as a fault and will lock the substation out and kill your power again. That's why it generally takes longer on ice storms than hurricanes (except for those wiped out or near the initial storm surge areas) to get your power back on, because we have to heat up section by section instead of the whole feeder at once like in the summers.
Of course summer time can be rough too because everyone has their a/c's on and we are picking up too much load that can cause problems as well.
Plus the transmission grid is so old and out of date they are beginning to not being able to handle these huge loads causing brownouts.
But the main reasons are they try to keep the load down during peak hours. Cooperatives really give them out because it costs them a ton during peak hours. Companies like TVA and Alabama Power can really put it to you when you are hogging power during peak hours and they really nail companies like the Cooperatives and companies that buy their own substation's but still have to buy power to keep the sub hot.
They would really be more successful getting the word out more but installing something similar but only shows what hours you would be cutting everything off, etc. and show the customer how much they would exactly save, etc. and more people might would buy in.