Fast charging 2.0: 7V×2.5A, 9V×2A or 12V×1.5A?
So it's, "I want 1.66A, please increase the voltage until 1.66A is reached, I will deal with resistance control".

No, it doesn't work like that. To be able to efficiently (fast) charge a single cell (3.6 - 4.2 V) battery from more than 5 V, a switching charging controller is needed.

A switching charging controller is basically a switching converter (a DCDC converter) where voltage and current are controlled using feedback and a microcontroller to charge the battery.

Only if that switching charging controller finds that it is unable to provide a certain charging current to the battery, due to the input voltage being too low, then it will request a higher input voltage.

Due to the switching nature of a switching controller, the current at the input side (coming from the adapter) and the current charging the battery, are not the same. A 100% efficient switching charger can for example use 9 V at 1 A and using that charge a battery at 4 V at 2.25 A. Both equate to 9 Watt of power. Note how "only" 1A flows through the cable while charging happens with 2.25 A !