It's not completely unexplained. Roughly speaking you can get that power spectrum in the limit when you are adding up many different events where the magnitude of the event is inversely proportional to its likelihood (and in practice, there is a limit to the magnitude of the events that will cause it to level off at some point, but for some processes this is not measurable even over decades). The main mystery in most cases is what exactly is the physical process that is causing it. For some electronics it looks like it is due to trapped charges sometimes tunneling around, but it doesn't explain every case of it in electronics let alone everything else. Convective thermal effects can also be a good candidate in a lot of systems, since turbulence also has 1/f noise properties.

(Also, the low frequency range on a DFT can look weird for reasons other than noise: it'll also tend to rise up if there's any longer-term structure to the signal as well, so you need to be careful interpreting them blindly if you're trying to measure noise)