TPE T1 and T2 are too old and way under capacity. T3 is taking a long time - bidding issues, corruption, cost overrun related design changes, etc. Taiwan is not as good as Mainland China when it comes to hardware/infrastructure for sure and all the other neighboring airports HKG, ICN, NRT/HND are much nicer.

T3's North Concourse is open with 8 gates. That will help. Some flights use it but you still have to do all the processing in T2.

Inbound carry-on check is limited to certain countries that have agriculture related issues. From North America, for example, there is not that check. In fact, if you start from the US and connect in TPE, you don't even have to go through security again.