What you say is certainly true, but the problem is that Taiwan doesn't have the means of delivering a nuke to Shanghai or Beijing. Taiwan is in the south, it only has missile capabilities of reaching Fujian province, which is mostly rural.
Well, I might be wrong, but I thought Taiwanese industry would be capable of producing missiles with adequate range. I'm talking about technological capability to produce, not whether they can legally. IIRC South Korea was pressured not to produce ballistic missiles by us a while back. Maybe we've got something like that in place for the ROC.
I don't know why we're so reluctant to share technology with Taiwan (they're still using upgraded Kidd-class destroyers IIRC). Are we behind them or not (but that's another issue).