Looking at the footage, they easily could have made the tank bigger if they just used all of the space available and didn't need to be able to "see" them from outside their tank. All they would have needed the aluminum for is to keep water out of where water shouldn't go and regular aluminum (or other material) would have worked just as well.
I thought they paid for whatever they used (plexiglass?) with the recipe for transparent aluminum.
Although it could just be that I'm forgiving the poor writing.
And if humans were in fact the source of Starfleet's knowledge of transparent aluminum then it'd be an instance of a causal loop, of which there are many examples in fiction.
Hell, there's several examples just in Star Trek.
(The answer of course is they're building an aquarium tank, and aquarium tanks are see through or have windows into it so humans can spectate. If they wanted to just bring whales back, they probably would have just flooded some crew room.)
It seems logical to me - it just had nothing directly to do with their whale-transporting plans.