I agree that the frigates and corvettes are more cost effective and more expendable assets for ASW patrols.
If you don't mind me nitpicking a bit: if I recall correctly, about a third of the Type 54A currently in service do not have TASS, and of the remainder, they do not have VDS although they do have TASS. That said, I don't know how up to date that info is, so maybe VDS has been installed.
The earlier ones all have TAS, so no ship does not have TAS. A third, which are the earlier ones, do not have VDS. Don't know if there has been any retrofits on the earlier ones yet. The Maanshan 054 refit might have installed one.