Active anti-torpedo weapons remain ship self-defence systems

Would active anti-torpedo weapons create a specialist torpedo-defence destroyer?

No. Their engagement geometry makes them local self-defence systems for the threatened ship.

A separate torpedo-defence destroyer would not solve the problem. The geometry and short engagement time of an incoming torpedo make the interceptor principally a local self-defence weapon. It therefore belongs on or close to the threatened ship rather than on a distant specialist escort. Anti-torpedo systems resemble close-in defences more than area air-defence missiles.