Would welcome opinions on how useful ASW rockets like the ELMA, Bofors 375mm and Russian RBU series are, given that these are short range weapons and are useful mostly in littoral conditions? Were these rockets actually designed to deal with subs in shallow waters or, as has been mentioned in a defence blog, to be used to against incoming torps? ASW rocket launchers were confined mostly to navies that had to work in littoral enviroments like the Soviet navy and Swedish navy and by navies that wanted a basic ASW capability but did not or could not afford to spend on torps.
The best answer I have is it depends. It is worth noting though that anti-submarine rockets/mortars did see widespread service with the USN, RN and other Commonwealth navies during and after WWII. The US ended up using AS rockets until the 1960's when ASROC entered USN service. The RN and various Commonwealth Navies kept A/S mortars in service into the 80's and 90's in some cases.
As I understand, A/S mortar or rocket systems remain useful in some specific circumstances. The first is that such systems are not especially useful for engaging deepwater targets, but are good for targets on or near the surface. Secondly, they can engage targets close to the launching vessel, with the max range ~6 km, but many of the systems only have a range of 1 km or less. Lastly in areas where there are 'difficult' sonar conditions (the Baltic for instance) which can interfere with the sonar aboard a LWT, then the ability to volume fire upon a contact can be useful.
A/S mortars and rockets still have a place in the inventories of some navies, but that is due to the environment in which their respective warships operate in.
-Cheers