For that matter, I bet Japan has them. If the conflict between Iran and Israel goes nuclear I could see Taiwan also developing their own. The proliferation is only restricted by time, money, and expertise.
NPT countries such as Iran can also acquire nuclear weapons without braking the treaty via Nuclear Weapons sharing[1]. This is how Germany, Turkey, and Belarus have nuclear weapons. If Japan or Taiwan wanted nuclear deterrence that is a route available to them (maybe that is even one of the goals of the potential Pacific Partnership military alliance; This is how Taiwan had these horrible weapons in the 1970s). It is probably harder for Iran though as they lack nuclear capable allies, but for e.g. Saudi Arabia, or Iraq, they could probably keep some USA weapons in at one of the many USA military bases (though I doubt Iraq would actually want that).
But you are wrong to omit politics as a barrier for proliferation. The NPT is strong, it has and most countries either comply with it, resign from it (North Korea) or don’t sign it. If Taiwan wanted to develop their own nuclear weapons they would need to resign from the NPT and potentially make any military aid from the USA infinitely harder in the process. I think their best strategy is to do enough nuclear research and have enough nuclear infrastructure so they are on the threshold of being nuclear capable without ever stepping over it (I think this is actually their strategy; as is Iran’s) that way they get the benefits of the NPT while still offering some nuclear deterrence, as in “we can develop them quickly if the need arises”.