I didn't think Sheffield had that big of an aluminium problem - the Type 21s, yes, but not the 42s.
EDIT: According to this site aluminum wasn't a problem in the Falklands, owing to the Type 42s being steel built, and Ardent and Antelope being so badly hit they'd have sunk whatever their construction.
True, but the ensuing fire is what led to the disuse of aluminum in warships. Anyway,
To be honest the Sovereign class, I don't really like it. It's just that you could easily build a small squadren of ships with equal abilities. Now if you had the squad you could have multiple ships to handle multiple situations. With the Sovereign, you're stuck with all that in a single place. If you need the a fraction of the firepower to deal with a situation in one system but need even more firepower in another system a Sov could only deal with one at a time, but a squadren could deal with both at once. You should never put all your eggs in one basket. But it is beautiful in apperence so it's not all bad.
We've seen time and again that with the Starfleet starship design ethic, bigger is better. Sure, you could build a squadron of ships with equivalent total firepower, but each ship would have considerably weaker shields; weaker SIF; less ammo capacity for torps; less available auxiliary craft and certainly no captain's yacht; less crew facilities; less crew capacity in general which could lead to overworked crews via longer emergency duty shifts; less raw replicator material; less impulse fuel; less AM storage; etc., etc.
Plus, she was the U.S.S. Enterprise - she HAD to be a big honking mother.