bintananth
behind a desk
If you want an "I can do everything" general purpose ship it's going to be extremely expensive and the budget is going to be "yes".All the Treasury-class was was rebadged Eries, and while they were excellent ASW boats, they were useless at anything else. Also note that the 'kill rate' is deceptive, there were a small number of Treasury-class ships, and they served longer than the various DE classes of which there were an order of magnitude more. They sank 4 enemy submarines between all 7 ships for the loss of 1 of their own.
The problem with using lengthened Coast Guard ships (I'm assuming you are talking about the Legend class?) is the 28 knot maximum speed, the CODAG propulsion plant, and that they are actually relatively lightly built (the decks are only stressed for up to 57mm guns, for example, rather than 5").
While they meet DC standards, and can be upgraded to a decent Frigate, they are FFs, not DDs.
I'd start with a Flight III Burke hull, delete everything above the weather deck, a new superstructure featuring a lighter radar suite optimized for self-defense and surface action, better integrate the towed array rather than have it as an afterthought, duel 5", 1 fore, 1 aft, a pair of 16 cell VLS systems for a mix of ASW, Anti-Ship, and Land Attack missiles, 2 of the same lateral VLS arrays used in the Zumwalts loaded with ESSM quad packs for self defense, since by the time any such ship could be built we'll have more programmatic experience with the IPS (once they ironed out the bugs on the Zums, the IPS became quite reliable) that wouldn't be the One New Thing, instead I'd install a suite of laser-based anti-missile/drone systems as the 'One New Thing'.
There's a reason most ships have specific roles. A battleship isn't launching an airstrike and an aircraft carrier will be told to "be somewhere else" when a gunfight starts.