For Alishan, you don’t need one; just the entry ticket you buy at the checkpoint.
What ‘nearby areas’ are you going to? For Tatajia, a pace with a good view of Yushan, you don’t need one.
For Yushan itself, you do.
I have heard that the easiest way to do Yushan itself and other high mountains for which you need a class A permit is to go with an organised group; perhaps a commercially run one that a travel agent could hook you up with. They can sort out the required permit and also arrange food and everything, which seems quite convenient.
3 friends are going to do Yushan at the end of October, but renting their own guide and going as an independent group; that is; not as part of a larger tour group. I think they told me that paying the guide will cost around 3000NT per person, but that he/she will organise a lot of things for them and of course, being a qualified mountain guide can easily get them the permit.
A figure of 3000 metres is sometimes quoted as being the threshold for needing a class A permit. I think this is not hard and fast, though, as driving over the Central Cross-Island Highway takes you well over 3000m with not a police checkpoint in sight.
According to the Lonely Planet, however, going to some parts of Maolin in Kaoshiung county requires a class A permit although it’s well below 3000.
I’m not too interested in the philosophy; I imagine that for the high mountains the intention is to prevent fatalities. As several people die each year in the Scottish mountains due to inadequate preparation or getting lost, requiring trekkers to take a guide here seems fair enough. I don’t think that going to such places is a right; it’s more of a privilege.