There is a major factor which is either being overlooked or ignored in the above scenario, and that is that ASW is a layered approach. If an ASW is investigating a possible contact 60 km away to the north, that would usually be considered in the middle layer, where most contacts would be persecuted when possible. If a threat was then detected 20 km to the south, that threat managed to evade detection until it was within the inner most ASW layer, and well within the effective engagement ranges of a number of sub-launched weapons.
To carry out ASW operations effectively, it would require multiple assets working together centered around and protecting either a key area like a port or choke point, or a task force. With that in mind, the direction is less important than how close a sub can get to what is being protected.
Not really, but on re-reading I can see in the most recent set of posts I did not make something clear. The most effective ASW platform is another sub, and a good sub, with a well trained crew, can often evade, elude, and otherwise control their engagement with 'targets' as surface vessels as sometimes referred to as.
From an ASW ops standpoint, if a hostile submarine has managed to close to within that third/inner most layer, where the surface vessels are, then the ASW force has already effectively lost the engagement. A system like ASROC-VL is still only useful within that inner most layer and the max effective range is still something like 20+ km short of the effective range of a number of sub-launched weapons. The reason why ASW ops want to have neutralized hostile subs by that 2nd or middle layer or before, is to prevent the hostile subs from being able to engage surface vessels.
To provide a little bit of context, an ASROC/Mk 46 combination would have a max effective range of ~33 km, which is about a two minute flight for a sub-launched AShM like a UGM-84 Harpoon., and well short of the 100+ km max range for Harpoon. It is also several km's short of the effective range for a Mk 48 ADCAP heavyweight torpedoe on a high speed run. Given how difficult it can be to detect a well-running boat with an experienced crew, the first indication a surface escort might have that a hostile sub has penetrated the outer ASW screens might be when the sub launches missiles and/or heavyweight torpedoes. With that in mind, a two minute window to detect a sub-launched AShM, track the AShM back to it's point of origin, detect the launching submarine, generate a targeting solution and then launch an autonomous counterattack using an ASROC with a homing LWT, might be a bit too tight. This also raises the notion of what might be a better value, a VLS cell which might possibly be used to launch a relatively short-ranged counterattack, or using the VLS cell to carry/launch something which would defend the surface vessel or another ship.