I think even if HSR did go right to the airport, there would still need to be a dedicated Taipei-Airport line of some sort.
For various reasons, HSR doesn't have the capacity needed for Taoyuan Airport's planned growth.
-Headway between trains is too great (way more than 3 minutes, because you can't run 300kph trains close together).
-Trains are not set up ideally (narrow plug doors in vestibules, lots of reclining seats instead of luggage racks, only 3 non-reserved cars).
-Taipei station doesn't have the capacity to turn around lots of trains. Nangang will be slightly better.
None of Japan's main airports connect directly to Shinkansen either.