Actually, that is exactly how ASW is done by ships using TAS/VDS, especially in a formation like a CSG or SAG. Google "ASW sprint and drift". What is not wanted is a sub right under your nose about to kill you. It is certainly possible when other ships in your formation are covering your ass so that you can do the job of proper ASW. Which again is sprint and drift using your towed arrays. And helos. And SOSUS. And everything else you can bring to the table.
Hallelujah! As I was trying to explore at the outset the traditional "PLA-Navy can't find subs for love or money" mind set may need revision because they can and that's why they have an extremely long range ASW missile.
They haven't, because they didn't bother to. As I hinted above, take a look at the Common ASW Standoff Weapon (Sea Lance) in the 80s. It got dropped with the dissolution of the USSR, and the same thing happened with most other ASW and ASuW projects (to the point that today modern US destroyers don't even carry Harpoon missiles). This doesn't mean that there was a trade-off study for the useful range of the system. Case in point, the Soviet Union did field the 50km range Snowstorm/Metel system based on the Malakhit ASuW missile.
The Sea Lance never left the drawing board and was suppose to have a nuclear warhead so rudimentary detection was sufficient, likewise the Metel also had nuclear tipped option. In both instances they're nuclear capable cold war weapons and the extra range is eminently useful! China has a "no first use" stance which I am prepared to believe so I don't think they would be popping nuclear warheads onto their ASW weapons.