Interesting video, I just have a few nitpicks.

The problem is not that the piano has too many strings, it's that the notes are fixed. The same is true for any string instrument with frets, like a guitar, or wind instruments with fixed holes, like a flute.

The video also refers to the fact that equal temperament allows playing in any key, but doesn't really explain why that's important or what the tuning has to do with it. (Short answer, before equal temperament, different compromises were made in which notes were out of tune with respect to which others, and the schemes commonly chosen only allowed some of the keys (as in "c major" not the physical key) to be sufficiently in tune to be usable.)