I really don't understand why it doesn't matter which one is chosen. If we are solely using a romanization to assist people in learning Chinese and to use as a transcription tool, it still makes sense to chose the romanization that most non-native Chinese speakers or non-Chinese speakers (the only people who make regular use of the romanization and transcriptions) are readily familiar with: Hanyu Pinyin.
As one of the large number of foreigners on this island that utilized Hanyu Pinyin when learning the language, I would accept a standardized Tongyong system being universal throughout the country, but it would be unfamiliar and I would have to do a bit of research in order to make sure I know exactly what sounds are being transcribed. If Taiwan made Hanyu Pinyin universal, I would instantaneously know which sound is being transcribed every time (without the tones, of course). I'm not unique. Virtually all Chinese-speaking foreigners in Taiwan are in the same boat.
So yeah, Tongyong kind of gets the job done...but Hanyu Pinyin gets it done with additional advantages that Tongyong doesn't have (it's very wide familiarity among Chinese-learners).
If Taiwan goes with Tongyong, foreigners that would like to be able to type in Chinese would still have to learn either Hanyu Pinyin or Zhuyin since I am unaware of any decent Tongyong input for Windows or Mac. Perhaps they exist but I doubt they are very well developed and also doubt that there are more than a handful of people in the world actually using them. Also, foreigners learning Chinese would still likely have to learn Hanyu Pinyin since a LARGE majority of Chinese learning materials utilize it.
Again, yeah, Tongyong can be used to transcribe Chinese just fine...But why would one choose it over Hanyu Pinyin when there are so many additional advantages to using Hanyu Pinyin? You could kill one bird with one stone using Tongyong, but you could kill a half-dozen birds with one stone using Hanyu Pinyin.