Zhuyin came first, by four decades
The Commission on the Unification of Pronunciation convened in 1913 and drafted the 37 symbols that became zhuyin, chosen and shaped from archaic Chinese characters (the full story of each symbol is here). The system was officially promulgated on 23 November 1918, and from that point it was the standard phonetic system taught throughout the Republic of China.
Pinyin did not exist yet. It was not developed until 1958, in mainland China, as part of the newly founded People’s Republic’s literacy campaign. By the time pinyin was invented, zhuyin had already been the standard for forty years. There was no earlier, neutral moment where Taiwan chose zhuyin over pinyin. Pinyin simply was not an option yet.
1949 split the two systems permanently
When the Republic of China government moved to Taiwan in 1949, zhuyin came with it as the entrenched, uninterrupted teaching system. Mainland China adopted pinyin as its new official standard in 1958, replacing zhuyin there. From that point, the two systems simply diverged along with everything else: Taiwan kept refining and using zhuyin, the mainland built its literacy and typing infrastructure around pinyin.
Neither side had a strong reason to adopt the other’s system afterwards, and Taiwan in particular had forty years of head start invested in the one it already had.
Switching now would mean rebuilding literacy education itself
This is not a matter of reprinting some textbooks. Zhuyin is how Taiwanese children learn to read at all: the first weeks of first grade are zhuyin-only, before a single graded character appears, and every character a child meets after that keeps its zhuyin annotation for years (this is covered in more detail here). Dictionaries are alphabetised by it. Standardised tests assume it. The default keyboard layout sold on every phone and computer in Taiwan is built around it (the layout itself is explained here).
Switching to pinyin would not be a spelling change. It would mean retraining a century of teachers, rewriting the first two months of every child’s education, and replacing the input method an entire country types with. Countries generally do not do this to a working system without an overwhelming reason, and zhuyin is not a broken system that needs fixing.
Pinyin does have a role in Taiwan, just not this one
Here is the part that surprises most learners: Taiwan does officially use Hanyu Pinyin, the same pinyin taught in mainland China, for one specific purpose, romanising place names and street signs for visitors who do not read Chinese. The Ministry of Education approved Hanyu Pinyin for this in September 2008, replacing an earlier system called Tongyong Pinyin that had been the official standard since 2002.
Even that switch was not clean. Several city governments kept using Tongyong Pinyin on their own signage rather than adopt Hanyu Pinyin, so which pinyin romanisation you see on a street sign in Taiwan has depended, in practice, on which city you are standing in. Zhuyin has never had this problem. It has been the single, uncontested teaching standard since 1918, with no competing system and no city-by-city inconsistency.
Romanised signage and classroom teaching are two completely separate questions in Taiwan. Pinyin, in one form or another, has been argued over for signs. Zhuyin has never seriously been argued over for how children learn to read.
There is a political dimension too
Beyond the practical cost, pinyin is closely associated with mainland China: it is what is taught in mainland schools and printed in mainland textbooks. Zhuyin, by contrast, is bound up with a century of Taiwan’s own separate educational history. That association is not neutral in Taiwan, and adopting the mainland’s system for something as basic as how children first learn to read is not a purely technical decision there, whatever the practical merits of either system on their own.
Will Taiwan ever switch to pinyin?
There is no serious movement toward this, practically or politically. Zhuyin works, it avoids the Latin-alphabet misreadings that trip up pinyin learners (covered here), and it is embedded in everything from school curricula to phone keyboards. For anyone learning Mandarin specifically for Taiwan, zhuyin is not a legacy quirk to work around before getting to the "real" system. It is the system, and it is not going anywhere.
Learning it is still only an afternoon’s work; the two-hour guide covers the whole thing in order, the chart covers every symbol with audio, and the app is where it actually sticks through repetition.