The soulstones were meant to be able to trap the Three entirely as Tyrael and the Horadrim lead us to believe. However, it is actually revealed (Act IV in D2) that Izual taught the Three to corrupt the soulstones and perhaps use them as a tool to amplify their powers. One can surmise that though the soulstones seem to be able to lock the Evils in a physical location they cannot contain the Evil's will and essence from seeping out. In this light, Baal's need to recover his soulstone was because part of him was still trapped within it and that he was not "whole" without it.
We are told by Tyrael that the Evil's souls can only be destroyed by smashing their soulstones on a special forge (D2). Given that he is unaware of the Three's corruption of the soulstones, in reality, destroying them would actually just release their souls as suggested in the D1 manual. Naturally, this is a bad thing for the Evil's because they need a corporeal form (either a soulstone or a human body) in order to do the things they do in Sanctuary. Shattering the soulstone kind of puts them in a limbo - they're not dead but they are effectively powerless and floating around until they can enter another vessel. I assume that entering Sanctuary is a difficult task for the Evil's to do on their own (I think the D1 manual says something about this) unless, I guess, a human actively summons one into an appropriate vessel. I assume that's how all the other lesser Evils like Andariel, Duriel and Belial made it into Sanctuary.
Because Baal's soul is trapped partially in both Tal Rasha's body and the soulstone, both need to be destroyed to release the soul. However, Tyrael mistakenly believes that destroying both would physically destroy Baal's soul as well. Since the Worldstone is corrupted by Baal's soulstone, it makes sense for Tyrael destroy it since it potentially is a conduit for Baal to still exist even with the destruction of Baal's (or Tal Rasha's) body.
Now we get to D3. The Black soulstone (which is no doubt a terrible plot device by the way) is a human creation and one that is not part of the Worldstone like the other soulstones. Because it has no real qualifier for its importance (it was created by someone suffering delusions of grandeur after all), I suppose that's the reason why Cain does not talk about it. It's also likely that the Black soulstone does jack-all in containing anything since it needed Leah to shore it up.
It is incorrect to think that Adria had sucked up the souls with the Black soulstone by first fixing it and then breaking it apart for us to find again. The cinematic clearly shows that Kulle only becomes aware that the demon souls are in there once he completes the Black soulstones and you see all those floaty things start flying into it. It appears that Adria only gleans enough information about the Black soulstone to somehow tag (I guess that's why they call it magic?) the still floating and dormant souls of the Evils (she had 20 years to do it don't forget) to make a bee-line to the Black soulstone once it has been finished. She actually states this herself.
Finally, we can assume that destroying the Black Soulstone would not actually destroy the souls contained within it. It didn't for the original soulstones (and rightly so considering they were already corrupted to begin with) and it shouldn't for the Black one either (which is really a cheap imitation of one by the looks of things). Still, destroying the stone is still preferable because the Evil's souls would be dormant and powerless as I had mentioned previously to just turfing it off to the side as is shown in the finale. Sure someone can re-summon them or reform their souls into another vessel but at least that will take more time than leaving them in the Black soulstone which is known for barely containing them at all and, as discussed previously, is potentially a conduit/vessel for their powers to seep through immediately.