Does it really take that much effort to synchronize the grid's
frequency?

To change the frequency they have to brake or accelerate the generator. What
I can't understand is which station is in charge of monitoring the frequency
and issuing commands to other power stations to speed up or slow down?

Frequency variation is not a big deal. When you have a power outage, the
voltage and hence frequency go to zero in a haphazard way. So if line
frequency variation would cause chaos, power outage should cause many times
the chaos.

But we have been living with the ocassional power outage, I think the minute
line frequency variation is not going to do any worse than power outage. In
fact it probably won't affect anyone at all.