Here are my five cents.
I have been on buses of that company, three times if I remember correctly, two times to Yilan and from there the Mingchi and Fushan (transferring to smaller buses for the mountain roads).
I think Wuling Farm is too far for a day trip from Taipei and the road is quite curvy once you leave the river valley. Also quite a few cabbage trucks on that road so you have to be very alert. So I would not have gone on that kind of trip, because you sit in the bus for most of the time and only spend a few hours at the destination.
Having said that, the drivers don't actually drive all day long. I guess, it's 3-4 hours to the farm from Taipei. Once there the driver can rest for 2-3 hours while the passengers visit the farm. On the way back, they most likely made a longer stop in Yilan for dinner or buying local produce (that's how the company makes some extra cash). I think there is enough time for the driver to get rest, provided he uses that time wisely.
The tours that were offered by that company were very cheap and they offered different trips to all kinds of locations every day. Quite well known among locals, especially retired people without their own means of transport, who like to travel in Taiwan.
Based on the prices they offered, it does not surprise me that the salary of the drivers were low and the buses were not in the best of conditions. The scope of the operation kind of convinced me that they had a certain safety standard in place.
I would put the accident under the category Accidents Happen (especially if law enforcement is not strict). You can always improve safety, but you'll never prevent human error.
A few things that definitely should change is enforcing existing laws, and if the laws are impractical, make them better. Everyone is talking about automatic driving these days. Why not first equip all buses with technology that can aid drivers (warning signals when she falls asleep, when speeding, when getting close to the side of the road, when keeping too-low distance to the vehicles in front...) There is so much room for improvement.
One thing that always freaks me out is that so many car drivers forget to switch on their head lights when it gets dark. Every car maker should be forced to put a warning signal into each car that reminds a driver to switch on the lights, or it should be switched on automatically.