The practice of taxiing with one or more engines shut down appears to be pretty common with turbines (jets and turboprops). I've been on dozens of airline flights where that was done. Airline Captains are constantly under pressure from their companies to save gas. Turbines are great because they are pretty much flight-ready as soon as the start sequence is completed.
On the other hand, reciprocating (piston) engines require a bit more preparation. Unless they have just flown and are still hot, they typically require at least a couple of minutes or warm-up time to get the oil and cylinder head temperatures up and stable. Recips don't like thermal shocking (going from cold to hot or the reverse in a short period of time). In addition to the above, recips typically need to have magneto and propeller checks done at some medium power setting, to ensure that the dual ignition systems, prop governors and propellers are all working correctly. That's why you'll generally see recip airplanes spending several minutes on the "hammerhead" near the end of the runway doing engine run-up checks.....whereas the kids with the jets just get to the end of the runway and go. Jets are easier to manage too. They have just one power lever for each engine and you can pretty much move them as fast or as slow as you like, because there is typically a computer between the throttle lever and the actual engine. Recips have three levers for each engine......throttle, prop and mixture....and they don't like it when you move any of those abruptly.
/Kevin Madore