Maybe as a sole destination, it would wear out over a week. But you would need a guide: road signage is abysmal to non-existant. The right kind of goat tracks are everywhere, but knowing how to connect them takes experience.
that said, the weather is also a beast (as for Taiwan in summer, although maybe not as hot. certainly as or more humid!).
best seasons are May-June after the rain, and October -November after the typhoons and heat.
the best roads are all small farming and logging roads in the northern area, north of Nago, often sketchy surface and leaf strewn, but leading to great roller coaster rides or spanning vistas along ridge rides or even the north east coast: 100 km of constant 10 percent up and then down with minimal traffic.
and the cars tend to be observant and respectful, which is a pleasant change after Taiwan or Australia