How are they so useful and practical?
A Navy ship spends very little time, if anyw, actually in combat. A ship hasn’t fired an anti ship missile in anger since, what, 1988 I think? (Operation praying mantis). However, on a deployment, helicopters can be used every day. If you are near land or an aircraft carrier, which you probably will be, they can be used for transferring parts and personnel, picking up mail, they can be used to get a visual look at contacts you wish to investigate, and many other things. They are extremely useful in anti piracy operations. They are a ships best weapon against submarines(and really only weapon that has a chance).
Basically, they are useful for something almost every day. The same cannot be said of guns or missiles.
But that’s not being used as a “weapons system”.
True, and arguably in a “weapons” role for a wide definition of weapons systems, but not exactly out of the range of things expected for helicopters.
In what specific way? That’s not an explanation.
More explanation would help. Get far enough away from your ship to detect them before they get into their torpedo range?
But the statement was for their use as “weapons systems”. Your statement was:
You have not made a strong case for them as a weapons system or different from what “we think” they should be used for.
Yes, and directly engage the submarine with air-dropped torpedoes as well.
Helos can flit around dropping sonobuoys and utilizing their dipping sonar to locate enemy submarines. Their speed in the air is much greater than that of the sub, so the sub cannot easily escape if located. If a submarine is located, the helo can engage it with air-dropped torpedoes. Against a helo, a submarine can do little other than attempt to hide. It generally has no idea where the helo even is, exactly. The submarine has no way to counter-attack and engage the helo directly (although it can deprive the helo of a place to land if the sub can get close enough to the ship that launched it). 
Without a helo, a ship is limited to its own sensors, and will likely be in torpedo range of any sub that it detects.
Generally speaking, submariners do not fear surface ships. They are just targets. Submariners do fear helos, though. They’re like an annoying mosquito buzzing around that you can’t escape, which can potentially kill you if your luck runs out.
Has anyone actually hit a submarine with a helicopter-launched torpedo?
In combat? Not that I’m aware of, primarily because there hasn’t been a combat loss of a submarine since air-dropped anti-submarine (ASW) homing torpedoes were first developed.
I can only assume that exercise and test torpedoes have scored hits in weapons testing exercises, mainly because a completely ineffective weapon would never make it out of development and into production. That being said, the word on the street is that no lightweight air-dropped torpedo has been as satisfactory as the developers would like, as seen in the saga of attempting to replace the 1960s-era Mark 46 torpedo, first with the Mark 50 torpedo, and then with the Mark 54 MAKO torpedo. The latter reportedly combines the powerplant of the Mark 46 with the guidance of the Mark 50, but has still not been completely satisfactory.
That said, in a combat situation, an air-dropped torpedo would hopefully at least distract an enemy submarine even if it doesn’t score a hit, perhaps enough to interfere with its mission (i.e. a “mission kill”) and/or allow the submarine’s target to get out of range of the submarine, or give other assets the time to engage the enemy submarine.
With respect to “other assets,” there actually is one asset that is more effective against submarines than anything else…and that is another submarine. That is why U.S. carrier battlegroups always include a fast attack submarine or two.
Well, there was the Ghazi, but whatever blew it up certainly wasn’t a helicopter-launched torpedo. Thank you, though.
How well can anti-submarine planes do? They should be able to go faster, farther and launch more expendable sensors and torpedoes.
I suppose that helicopters can dip fancier non-expendable sensors which don’t have as good an equivalent in planes.
Quite kindly. For them.
By the way, I didn’t mention the comment about anti-piracy. Helicopters go faster and allow further ranging around the ships and fast assault followups or tracking to get ship assets in place.