How is this different from a regular timer thermostat which turns on exactly at the set time?
Our non-smart thermostat has trouble keeping accurate time and drifts a minute per month or so. That would spread the load out more because “6am” is a ten minute window.
If the demand rises over the course of 10 minutes, you get a small drop in voltage and the plant ramps up gradually.
If the demand rises by the same amount over the course of 3 seconds, you'll get a much bigger voltage drop and the power plant has much less time to speed things up.
There's further complexity because real power grids are the size of nations and have many power plants. If several power plants notice the voltage dropping and increase their production, a few seconds later you might have too much power. Then they might respond by cutting their production, and a few seconds later you have too little power and so on.
More than that, if the voltage drops too low, like from a sudden large power draw, you could get a brownout or even a blackout in severe cases. Voltage level is monitored and wild swings indicate instability which trips various safety systems.
Non-smart thermostats (even digital ones) usually drift on the clock settings substantially over time.
Even if most other thermostats have a timer feature, I guess they are not all turned on and set to the same time by default.
Older buildings have had the electromechanical thermostats you describe.