This is a great explanation. To add onto this, I would imagine a lot of non-musicians would wonder whether there's a good reason for equal temperament, as most songs in every genre utilize it instead of more consonant scales (e.g., just intonation).
There are two main reasons. The first is a matter of switching between scales, as in, many songs will modulate to out-of-scale-but-mathematically-related chords. As 12TET has each scale using the same notes, one doesn't have to tiptoe around shared notes which are 'slightly' off. The second is pure convenience: using a set of notes for each key (or pushing the root note a few Hz up or down) would be a laborious process.
With that being said, an interesting direction some electronic producers take is to experiment with scales, given how ubiquitous waveforms with integer harmonics are. Here's an example from Richard D James: https://youtu.be/pTn1tmhA8L8