If China has to battle Taiwan's submarines for control of the subsurface, it won't dispatch its entire submarine force to do so. China would, at most, send two of its attack subs in search of every Taiwanese sub. Were Taiwan to acquire the eight new submarines, that would distract, at most 16 PLAN submarines in a Taiwan Strait conflict. That would leave China 39 attack submarines to sink the ROCN surface fleet or Taiwan's merchant marines, or protect its own invasion force. Additionally, any ROC submarine that successfully carries out an attack on PLAN forces would be immediately sunk by PLAN submarines, destroyers, or sub-hunting aircraft.
This analysis ignores the fact that China's subs are on average, quite poor and poorly trained as well. They rarely put to sea and usually do so with the company of surface ships just in case. I sincerely doubt that the PLAN could put 16 effective attack submarines to sea to sink the 8 proposed Taiwanese boats under debate.
Nor do I think the PLAN's anti-submarine capabilities spell a death sentence for the Taiwanese boats. I'm not even sure the PLAN would be immediately aware of their own losses let alone the amazing ability to destroy modern subs with PLAN assets. Chinese naval warfare capabilities are not exactly advanced except for narrow bands created by buying Russian weapons. Even there the training won't be very good.
As for cost effectiveness, let me just add that as long as a single Taiwanese sub equipped with American-made Harpoons is at sea (or believed to be at sea), the United States will be able to maintain plausible deniability that American subs are not actually shooting at the invasion flotilla (we in the blogosphere can then marvel at the capabilities of the lone intrepid Taiwanese captain wreaking havoc on the PLAN surface fleet).
I don't know much about macro-economics, but I think buying those submarines and getting the possible use of the US submarine fleet is highly cost effective. Taiwan needs those eight submarines.
UPDATE: MeiZhongTai notes this post and is providing commenting space for the issue. For this I am grateful and thus far I am confirmed in my decision not to enable comments here. In my life I have been able to have friendships and civil conversations with lots of people who have different views than myself. Perhaps it comes from living and working in places where my views were always in a clear minority. A short stint in the military and my current job also emphasize nonpolitical activity in pursuit of goals above political considerations (And amazingly enough when I take those political quizzes I tend to show up as a "moderate" believe it or not--but I've lived in Detroit and Ann Arbor, so that tells you something about these places!).
But it drives me to despair when disagreements descend into the all-encompassing "you are an idiot in all you believe" line of thought. Some good points made in the comments, but some of the asides and out-of-scope arguments made mean I would have to embark on a complete defense of American foreign policy just to address friggin' subs for Taiwan. And commenting on just the narrow topic at hand might give the impression that I agree with the points I don't comment on. I don't have time for this level of "discourse." Strictly speaking, I don't have time to blog period! I'll have to be content to let readers decide on their own. I added my two cents and I'm happy with that.