1) Why did the US navy adopt only 'boost' gas turbine and not a cruise and boost gas turbine arrangement as adopted by the RN (alternatively with a diesel cruise plant).
The USN's transition to gas turbine propulsion was closely tied into the DX (Spruance) acquisition, so we really have to look at it in the context of that program. Because DX was specifically an ASW specialist ship, silencing was important and there was a contract incentive to hit certain noise targets. That ruled out CODOG (and eventually even diesel ship service generators).
Before DX (e.g., Project Seahawk), the USN had looked at a cruise-boost approach, but the poor efficiency of early GTs and some really demanding silencing targets pushed them to some really exotic options (regenerative gas turbines, turboelectric drive, etc.)
It doesn't look like a cruise-boost configuration was ever considered for DX proper, possibly because the US didn't really have a suitable available cruise turbine at the time and didn't want to develop one. Also, the way the ships were operated, it turned out you don't really need separate cruise turbines since you can run on a single turbine much of the time. That keeps the one running turbine at fairly high load, making for better efficiency.
Some novel plant ideas were looked at for DX, BTW. In theory, four LM2500s provide more than enough power for the Spruance, so the initial design from Litton actually used only three turbines and an electric cross-connect with motor-generators on each shaft. So one turbine would drive one shaft directly and deliver partial power to the other shaft via the cross-connect. But they decided that wasn't proven technology, and it added a bunch of weight anyway. So they went with four turbines and two entirely separate drivetrains.
1: has to do with ship size, probably. A 4000 ton frigate can be run with 2x10,000 shp cruise turbines, an Arleigh Burke needs 2x20,000 shp of cruise power.
The LM2500s in the Burkes are actually uprated to 25,000 shp each. But the most common cruise configuration (almost 2/3 of underway time) is actually trail shaft with one turbine driving a single prop and the other prop freewheeling. The Spruances were much the same.
