So there are a few things to dissect here. A number of years ago, there was a lot more emphasis on alternative measurments like impulse, square wave, CSD, ect. But over time it became much more clear that SPL frequency response is most of what you need when it comes to headphone measurments. Due to them being mostly minimum phase, time relevant measurments are most often consistent and predictable. So simplifying things to just frequency response removes a lot of confusion, and is more representative of audible differences when it comes to headphone measurments.

On to your point about speed. How fast a driver can respond to a signal, it's common to initially think about inertia and how mass causes some lag in motion, but when it comes to headphone drivers, they are so light and thin that most are capable well beyond what is required. Many drivers are capable of over 40khz, but the audible range is up to around 20khz at best. That means any thing within the audible range will be reproduced "fast enough". If it wasn't able to respond fast enough, you would see a drop in the frequency response and an increase in distortion. Similar to what you may see in some sub woofers when they try to play above their frequency range.

On to your point about playing multiple frequencies at once, it's good to look into fourier series. When multiple frequencies are played at once, the amplitude is all added together. So when there is a rise, the amplitude is added together, and if there is a rise in one frequency and a decrease in another frequency, it's subtracted. This means many different sound waves are able to be layered in a single motion, and your ear works as a fourier transform to separate the frequencies and phase from the single combined motion into its individual frequencies. So when playing multiple sounds at once, the driver can make seemingly simple motions, that contain all the frequencies needed to hear multiple sounds at once which is then separated into its frequencies at your inner ear and brain