Why is there a time-frequency precision tradeoff
why can I as a human hear lower frequencies sharply, but the FT cant?

No you can't. Human pitch discrimination at low frequencies is actually not particularly good. The &quot;sweet spot&quot; for human pitch perception is between 250 Hz and 4kHz and it gets rapidly worse above and below that. When tuning a bass instrument you typically try to reduce the fundamental and the lower harmonics as much as possible and emphasize the higher harmonics a lot since this makes it a lot easier to determine the correct pitch. A violin slightly out of tune makes everyone cringe: a double bass slightly out of tune is hardly noticeable.
So in this regard the human auditory system is no better than the Fourier Transform.