The problem for Taiwan's navy is that the biggest threat to them doesn't come from under the sea but increasingly comes from the air. And that's were they are weak.
The ROCN has to be ready for several scenarios.
First is conflict with the mainland. In such a scenario it is true that they will be subject to massive ballistic missile bombardment to try and negate their air force, their air defense, and any navy in port. But the ROC is prepared to defend against a certain amount of that, and absorb the rest, depending...and absolutely relying on...help from the east in the form of the US Navy. That will be their ultimate life line. The submarine threat is going to be one of, if not the most dangerous threat to that happening. So their ASW capabilities to stave off a blockade/picket line of submarines to their east will be absolutely critical. And these Perry frigates from the US, as well as their own builds, will be absolutely critical to that.
Second is the potential for conflict with smaller nations in the South China Sea. Some of these nations are going to have decent submarine warfare capabilities and the Perry frigates would be absolutely critical in any conceivable confrontation with any of those powers.
Third, patroling against piracy and asymetric threats from terrorist. While the Perry's ASW capabilities will not come so much into play in this scenario, their excellent sea keeping abilities, the fire power they have, and particularly their helicopters would also play an important role in those duties if required.
These US transfer Perry's will serve the ROCN well...but (unlike the local built Cheng Kung Perry FFGs) they will not be a strong anti-surface warfare vessel against other maritime powers who have their own strong anti-surface capable desttroyers, frigates or corvettes. That is, uinless the ROCN upgrades them and adds the ASuW missiles to them as well. Otherwise, the ROCN will have to rely on its missile boats, the Kang Ding FFGs, (and as stated) the local built Cheng Kung FFGs, or the Kee Lung DDGs for that.