In the early days of steam engine powered ships, wouldn't a system that intermittently injects high pressure steam above a wide column filled with water, thereby displacing the water and expelling it through a nozzle connected at a 90° angle with the bottom of the column offer better efficiency than ungeared steam turbines? A valve would then open letting the steam escape and the water surge back in to the previous level and the cycle would repeat.
If you did that, you've lost your steam. You have to keep it and run it to a condenser then back to the boiler. In the Titanic, the residual steam from the triple expansion piston engines was only 9 psi, down from about 215 psi. So I'm not sure what you had in mind by high pressure steam. These gearless turbines were blowdown turbines. The steam volume at this point was just too great to keep adding cylinders to the engines. The turbines were more compact.
What we are talking about, I hope -
But lets add a piston to separate the steam and the seawater. Now you can get your steam back, and you have what is called a free piston engine. What you need to consider now is the size. The Titanic's turbine was 12 feet in diameter and expanded steam from 9 to 1 psig. How big would a two stroke free cylinder have to be to move the same amount of steam? How big would the exhaust valves have to be? They quit adding cylinders to the Titanic's piston engines when they could no longer manage the volume of steam and the heat losses from the piping would sap too much energy.