Sadly the 45 could not be used like that - it was a wire guided sub-launched weapon. Plus it weighed six times as much as a standard ASROC weapon, the 46 (without the nuclear charge). The depth charges (Mark 101 and later a variant of the B57) were air dropped. There was a nuclear warhead for the ASROC, it was the W44 (the W34 was the one on the type 45).
The 45 really was there to deal with targets that nothing else could get - the very deep diving Soviet subs that scared the west so badly. Then they built their ADCAP models and the need for such a weapon went away. I think the Soviet version's stated use was to remove an aircraft carrier group. In either case they were basically only for use in a scenario that meant a) the sub would be killed for sure trying to stop the threat on its own and b) the consequences of the threat getting through were considered too high to pass up the opportunity to destroy it.