Perhaps you could clarify what you mean by having an ARC isn’t a requirement? Specifically, could you speak to how you did those tasks, and what companies and specific offices you went to in order to accomplish them? My experience without ARC is very different to yours.
I can say from experience that life in Taiwan without ARC sucks. Even if you have a visa, such as “language student visa”, which is really just a “visitor visa” with a footnote. The language student visa has a different rule set to degree student visa too, so they information you get will likely be conflated between the two. You can eventually get an ARC on a language student visa after having enrolled in 9 months (4 months complete, + additional three months already enrolled, of which they only come in 3 month semesters AFAIK) of classes. But there’s alot of gotchas. You need to visit two different government departments to get it, and they don’t talk to each other, so you’ll need to speak to both of them separately every time to get the right information, because you need both of their approvals to get ARC. I ended up getting erroneous information from immigration and the school, and it meant that I would need to leave Taiwan and start again.
You can’t get a phone number yourself. I tried on one occasion, and got one in my name but I had to have a Taiwanese vouch for me at Chunghwa. Even then, you have to use the older, slower 4G, despite 5G being available. And the maximum length of SIM service is 180 days. You can’t even make international phone calls from that number, even if you ask to add a package to do so. After that you can’t renew it, you need to get a different phone number. I tried later to get a Chunghwa SIM, and they said because I didn’t have enough days left on my extension I couldn’t buy a new one. This is despite the fact that you can only get 60 day extensions, and you can’t renew them more than 14 days in advance. How bizarre when phone companies play like they’re immigration. At that time, I tried to go to every phone shop, and none of them wanted to help me, all suggesting that I get a friend to sign up to a 2 year phone plan. So, the reality is, you’ll have a very tough time getting even a phone number.
Yes, you can get a temporary ID number from immigration, but none of the companies in Taiwan recognize it. No banks recognize this at all, except for the Post Office Bank. If you go to a language school with a relationship with a post office, you might be able to open a Post Office Bank account. But you’ll need a Chinese name and a stamp first, before you get the immigration document. But be careful, you might end up unable to access your money if you end up with any discrepancies in your paperwork or phone number not working later.
There are many many many things you can’t do without an ARC, and life will be very difficult.