In Taipei at least, they only started to come ID after that one cop was killed. They mostly came to flex their powers and to disrupt business. A complete waste of resources, you don’t need 50 cops coming on a Friday night to do ID checks.
Before I went to China, I went one step further and had a colour photocopy of my passport notarised by a notary public, authenticated by DFAT and authenticated by the Chinese consulate. Completely overkill and a big waste of money but it was fun and I got a few colourful stamps. But I really didn’t want to carry my passport around with me outside for fear of losing it and I figured if I was ever asked to produced it by a policeman there’s no way he could give me shit for producing an unauthenticated photocopy. I still have it lying around somewhere.
Does this link work? If not, you might find by googling “未隨身攜帶外僑居留證或護照 裁罰”.
It seems a presentation file by NIA at 臺南縣工業會, and the theme may be management of blue collar workers.
Slide 20 says violation of Article 28 would be fined based on Article 85.
I’m not sure whether the info is up-to-date.
It’s a different law here. In the UK and US, you don’t need an ID card on you (and there isn’t a national ID card programme in either country). But here, and in some EU countries, you are meant to have ID on you all the time.
I would imagine leaving your ARC at home and using your NHI card as your ID might be OK because the cops can cross reference your ID number on the NHI card to check your address, immigration status etc.
I always used to carry my ARC/APRC, my open work permit, my driving licences (Car & Scooter), My NHI Card, My Citizen Digital Card & my Scooter’s registration in my wallet everywhere I go…these cards are pretty small and fit easily into my wallet so I don’t find it cumbersome carrying them on my person at all times…never carried my passport unless I needed it when opening a bank account or getting a cell phone contract. Nowadays my APRC has been swapped for my Taiwan ID but I still carry all the other cards with me (incl. the OPW…for sentimental reasons 
). I’ve noticed most Taiwanese don’t carry their original Taiwan ID with them, just a copy…for fear of losing it, but getting it replaced is so easy and convenient these days (takes about 30 mins max. at any HHR) that I don’t mind carrying the original on my person at all times.
I was in a club years ago when police were paying ‘surprise’ visits each night - I believe it was following the nightclub fire in Taichung. My ARC (APRC?) was in the Immigration Office for some sort of processing and I told police I could show a copy on my phone but he said it didn’t matter and not to worry about it.
I never carry any form of ID, even when driving, unless I know I’ll be needing it. Don’t have to worry about losing it and a much better chance of getting a pass for any ticketable offense.