Why an escort can defeat a U-boat without sinking it

Was Britain's mass deployment of escorts against U-boats an act of panic and desperation?

No; it was the planned convoy-defense method, and driving submarines away was a valid victory even without a kill.

Corvettes, sloops, destroyer escorts, and frigates formed the intended answer to the submarine campaign rather than a panic improvisation. They guarded convoys and attacked contacts when U-boats approached. Some classes, especially the Black Swan sloops, also accumulated strong submarine-killing records. Yet an escort's essential victory was forcing a U-boat underwater or away from the convoy, because safe merchant arrivals mattered more than adding a sinking to the escort's score. A U-boat forced underwater cannot pursue as effectively; surfacing to regain contact exposes it to aircraft and surface escorts.