Solar cell understanding of current vs applied voltage
It seems like your understanding is pretty much correct. There is just one clarification. The Voc and Vmpp are only slightly sensitive to irradiance. See attached graphs which are real DC data from one string in my grid-tie solar array. The grid-tie inverter logs data at 5 minute intervals.

As you can see, Vmpp does not vary much during the day. And its cloudy-day and sunny-day values are pretty close, all things considered. The depression in Vmpp on the sunny day is probably a reflection of panel temperature.
So it is possible to have an OK installation without using MPPT in some cases. But, in order to maximimize power over the full range of battery voltages, or when the battery voltage is not close to the solar panel Vmpp, MMPT charge controllers are required.
In general, some kind of charge controller is always required if for no other reason than to avoid over-charging the battery. But it doesn't always have to be an MPPT charge controller.