I think the basic idea behind targeting 120dB SPL is that 120dB SPL is often quoted as the threshold of pain on a lot of these "how loud things are" charts. So it's rather arbitrary target but safe to say, it's more than enough for an enjoyable listening experience.
I noticed that when discussing headroom and listening levels on this forum, people mean different things by "headroom" and "listening levels". For example, when someone says their listening level is at 80dB, what they usually mean it's probably 80dB based on absolutely and utterly nothing at worst and based on getting a microphone and putting it against their headphones at best, which is still so inaccurate that it's just an unrepresentative number.
As for headroom, some people use it as it's typically used in other contexts, they say they listen at 70dB SPL, their music peaks above the average level by 20dB, therefore they need 20dB headroom to reproduce the peaks which means they want an amp that can push their headphones to 90dB. In this sense, 10dB of headroom is only enough for music that has been considerably compressed or limited already.
On the other hand, what some people mean by headroom is that they say they listen at 80dB, their music peaks above the average level by 20dB, and they want 20dB (of unused) headroom above the peak levels, so they want their amp to push their headphones to 120dB. In that sense, 10dB of headroom is 10dB more than what is actually needed.