Id hardly say the constellations had a large radar array, capable sure, but not large.
I think you're misunderstanding.
Even though SPY6v3 doesn't take up a large volume in the ship,
getting those arrays up high enough to be effective requires a large ship.
The minimum install for a destroyer is likely SPY6v4 (24RMA antennas), and I expect that SPY6v1 (37RMA antennas) is going to be seen as the threshold capability (ie, bare minimum that the USN will accept).
I have no idea what the RN has for the comparable system to SPY6. I strongly doubt that they'd buy SPY6, simply as a matter of keeping the capabilities as something the UK can build. (And for the record I think this is a really good policy!)
Why do you assume theyre carrying any asrocs, limited in stock and hardly an effective weapon these days.
Because it's one of the very few ASW weapons the USN has
at all, and takes up a full missile cell when you're working out loading plans. Also, it's relatively fast to get to the location of a submarine and gives very little warning that someone is about to drop a torpedo on your head. No rotor noise, no 68hz tonal from those bastard P-3s.
They're limited in stock because the USN likely only has about 6 per ship that they have ever bought and more or less only expends them in exercises when a new ship is commissioned.
Literally the only other option the USN has for ASW is an airdropped lightweight torpedo.
Also, I'm using ASROC as a shorthand for "ship-launched antisubmarine weapon", whether it's the US RUM-139 VL-ASROC, K745A1 K-ASROC, Type 07, Ikara, RPK-6/7, SMART, or anything else someone has cooking of similar type and capabilities.
The Japanese Type 07 or Indian SMART would be the preferred systems, with ~30km ranges. RUM-139 kinda
sucks, range-wise.