Very good and detailed explanation!

I want to also add on the last part; often the difficulty is composed of all of those elements, because each single difficulty element scales very badly.

For example game that only focused on the precision and timing has some limits where the game just breaks because it is no longer possible to move fast enough to keep up. At this point increasing the duration (adding numbers) of the ‘encounter’ becomes a better way to increasing difficulty.

Good example of this would be “Through the fire and flames” in guitar hero. It already tests your precision and timing to the extreme, then adds a long song duration (7+ minutes)