Agree, you really can do nothing useful in that time given you must be back at TPE so early and it seems you will arrive somewhat exhausted.

IF you were keen to see Taipei AND you were well rested, then you could consider an all nighter. Check in at airport hotel, taxi to city centre, a couple of night markets, a wander around, taxi back. Wash, a couple hours kip and off you go. I did it once (except stayed in the Monarch Plaza, Taoyuan as my GF was a FA and was put there. She was keen to see a bit of TPE). It only worked cos she was mad and I was well rested. The flight times were similar to yours. I did say never again and it hasn't happened since.