That's right. There is no baggage service at Taipei Main Station, so you can't shop bikes from there.
As for rolling on and rolling off (i.e. unbagged), the Chinese-language page for taking your bike on the trains says this
Bicycles are not allowed to exit and enter the station at Taipei Main Station. Therefore, no tickets are sold from Taipei.
A riding buddy was just denied entrance to Taipei Station a few weeks ago when I failed to explain this to him.
Possibly he could have gone on with the bike in a bag--you couldn't the last time I tried about 5 years ago. But you have always been able to take the HSR with your bike in a bag from Taipei Main Station, so go figure.
It seems that the rule is that you can take a completely bagged bike at least on any local train and that most if not all of the west coast express trains have a Car 12 where you can put your bagged bike.
It's not just us. Here's a recent thread where a bunch of Taiwanese people are bitching about the rules are impossible to figure out and the TRA staff all have different versions.
mobile01.com/topicdetail.php ... 698613&p=2
Here are the service numbers
臺北運務段（基隆—香山間各站） 李少宜 小姐 (02) 8969-1108
宜蘭運務段（暖暖－漢本間各站） 王一涵 小姐 (03) 937-2973...(恕刪)
Whatever. I go all over Taiwan with my bike in a bag or not on the correct local trains and I avoid Taipei Main Station, which has always been highly bike hostile. It's actually easier to do it than it is too explain how the system works!
The overnight shipping service is generally the easiest and most reliable way to get your bike around Taiwan. I've been using it for 20 years. A good trick is to get on with your bike at a really rural train station with no staff and then ship your bike from the next secondary station with shipping service.