Last I heard, this was already being considered -- Congress has been kicking around building or selling Taiwan 4 Aegis equipped DDG's for a couple of years now. Another thing to take into consideration: these (Chinese Aegis ships) are air-defense ships with a limited ASW capability (to judge from the ASW weapons listed).
If I were Taiwan, I'd start stocking up on submarines. Chinese capabilities seem to have grown in amphibious shipping/heavy sealift and air defense. Perhaps this is a weakness that submarines can exploit.
Secondly, Tawian should also start stocking up on submarine-launched mines in order to deny the approaches to Taiwan, or if necessary, to mine the approaches to PRC ports. The PLAN still has the same basic problem: crossing the straits with a sufficient land force to invade, or a sufficient fleet in order to blockade. Mines would be a quick and cheap solution. Not a total one, but a start.
Finally, if I were Tawian, I'd start getting closer to Japan and India and forging some kind of defense ties. In the event the US Navy cannot get to Taiwan in time, having the Japanese/Indians in the neighborhood might come in quite handy. It also puts two additional, substantial threats on the Chinese flanks in the event of war over Taiwan. I'm sure the PRC has already thought over the threat from the United States, I wonder how they would think if faced by a US/Japan/India alliance, with a nuclear India right next door.
However, this is all bluster on the part of the PRC. I don't believe a war over Taiwan will start anytime soon because the Commies are really more interested in staying in power. If the shooting started over Taiwan it would unleash force within China that cannot easily be controlled if victory does not come quickly. if given a choice between staying in power or taking a massive black eye in a fight for Taiwan, the party can be counted on to protect it's own behind first.
Not only is the US rather undecided on selling Aegis equipped ships,the Taiwanese parliament seems lost too.The current proposals are to build the ships in Taiwan & use American systems on it.Anyway,even if Taiwan gets this ships(sold or built) in 3 or 4 years,it will take over an year for them to train officers & build up logistics for those vessels,given that they have never operated anything as big or complex.
The Type-052C's ASW capabilities appear limited,but they are easily the best the PLA-N has fielded ever & the more important point is,submarines are one area where Taiwan is hopelessly weak.Their current force consists of only 2 credible 1980s era Dutch subs & 2 American world war 2 era boats.One would have to be deluded to assume the PLA-N hasn't been tracking those vessels. & It is highly unlikely that they will get new vessels with all potential sub designing nations hedging their bets with the PRC.