They're more complicated (and thus more expensive) than propellers, but the real reason is that Pump jets are historically mostly used only for ships that need high speed at all times (such as submarines). Engines that power ships (or anything else for that matter) are most efficeint at a certain output and it isn't desirable to go high speed at all times for endurance/efficiency reasons.
On a DDG-51 Arleigh Burke Destroyer, the ship carries 4x LM2500 gas turbines that power the main propulsion system as well as 3 service turbine generators for ships sytems. 2 turbines are tied to a mechanical drive through the Main Reduction Gear Assembly, that is connected to the shaft and the propeller. The turbines have 2 speeds: off and on. And that's it. To control speeds, the ships turn on or turn off LM2500s... the faster they go, the more they use. At about 18-24 knots, the Destroyer is highly efficient and can go 7-10 days without refueling because it's using 2 LM2500s. At high speed (24-28 knots), endurance is 3 days (3 engaged). At "flank speed", 28-30+ knots, a destroyer can go as little as 9 hours before refueling (4 engaged). However below (15-18 knots) endurance is still `~10 days as 1 LM2500 and one service turbine generator is used. This is highly inefficient.
Presently the Burkes are starting to be refit with Hybrid Electric drives that will power the Burkes below 15 knots, and will add days to their endurance by allowing 2 of the 3 service turbine generators to handle propulsion at that speed and all LM2500s to be turned off.. Integrating a pump jet into this would be counter-intuitive - a surface ship simply doesn't need to go that fast all the time.
In fact, the high speed/complicated propulsion of the LCS class, which has Pump Jets, is one of the big problems with the ship.
More on this: http://www.defenseindustrydaily.com/...to-them-07142/
The Virginia class submarine, the Seawolf class submarine, and the Ohio replacement submarine use (or will use) pump jets. However they're all nuclear. They don't need to be refueled. The Ohio class and Los Angeles class do not use pump jets.
GE is working on it though for surface ships.
http://www.gereports.com/post/745451...-pump-jet-for/
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He'll be an Admiral by then, if he is still serving. The CVN-80 (USS Enterprise) won't be launched until 2023, commissioned until 2025 and likely deployed until 2027-2028.
The FY2017 budget by the way includes long lead in time for the Fourth Ford class carrier, after Enterprise. Since America is now a Amphibious Assault Ship, they should go with Midway or Franklin D. Roosevelt, or maybe, just maybe Arizona.