It depends on if you have family, mortgage, income tax, health insurance, labour insurance , decent clothes for work, money for eating and socialising with colleagues, phone bills, internet bills, electricity bills, fuel, bus/train tickets to visit family, money for purchasing a scooter and laptop and mobile phone etc. etc. Most of the people in Taipei who can afford to go out to restuarants and properly socialise are living in their folks homes.
None of the above are really discretionary in my opinion, they do not include extra costs incurred in this society including New years Hong Baos, wedding Hong Baos, contribution to parents and siblings. Don't pay them...forget about including in society here.
Accomodation is not 'dirt cheap' outside Taipei , it's still 10-20 NTD/mth rent for a small apartment, then most people . Cheap compared to most places of course.
There are some people who refuse to live in Taipei due to the cost, me included at the moment. But you must be aware of how dismal office jobs pay is outside of Taipei, 20-30k/mth is common. That's just 700-1000 USD/mth. Before tax and contributions. It drops really quickly outside of Taipei and Hsinchu. Yes don't be an office worker in Taiwan. There are some relatively well paid workers but they tend to be engineers or technical or professional people.
Yes it's possible to save some money in a place like Taipei, but only living a very stringent and boring type of life and ignoring the expected social aspect of work and your own family.