It would probably blow their minds at Shin Kong Bank to know non-Taiwanese don’t even need an ARC to open a bank account, just a Tax ID number (and passport)
https://www.goodlifetaipei.com/how-to-open-a-bank-account-without-an-arc/
EDIT: The link to the form no longer works (what a surprise), so here’s the link to the online form: https://niioa.immigration.gov.tw/NIA_OnlineApply_inter/foreignApply/foreignApplyForm.action
I’m a little late to the discussion but a lot of this issue started a few years ago when banks cracked down on the KYC rules (know your customer). They would be suspicious if you were opening an account and didn’t live nearby. The only other reason is if your work was nearby and there was a reason you needed it like direct deposit.
When I arrived a long while ago I opened 10 different accounts to see which bank I liked better and the banks couldn’t give a toss. Now they care a lot about the purpose of the account.
One example, I lived in Kaohsiung and have a first bank acct there. I moved to Taichung and wanted to open a foreign currency acct. The first bank near my work said I had to go to the branch near my house. I ended up going to the branch a few streets over from there and they did it. I asked the Kaohsiung branch if I should open it there since my ntd acct is there. They said no, since I didn’t live there anymore they wouldn’t open a new acct for me even though they already had an acct there for me for over 6yrs. A lot of stupid bureaucracy.
I had another bank look at me strange when i asked to open an account that the manager said I’ll open the acct but for 6 months no ATM card. Come in to do all banking. If your account is good in 6 months then we’ll consider giving you a ATM card.
So I went to open the bank account during lunch and I had my old ARC card (applied for my new ARC last week Wednesday) and they told me I can’t use the old ARC card, it has been cancelled. Soooo she phoned immigration and he said I must phone this week Thursday to see if my card is ready, and come pick it up early (1 week 1 day) and then go back to the bank to open my bank account. This is the hardest thing I have ever had to do in Taiwan… 
THESE are the times that try men’s souls
The bank must have a live up to date connection with a validity checker of the immigration database now. In the old days they just took a photocopy
Banks can be rather frustrating.
This know your client thing is also frustrating.
So far the only KYC I got was from mega bank on an old account. I left my salary part blank as that isn’t their business. So far nobody else has harassed me