Can anyone explain why the engine would be shut down taxiing in??
Saving gas is one answer. I agree that it's a questionable tradeoff in a lot of cases.
Another reason for single engine taxi is that many twins are overpowered in taxi with a light aircraft (and even more so in cool weather).
There is a classic trap involving single engine taxi and the takeoff warning horn. If you're in single engine taxi and stop the aircraft, you sometimes need a throttle setting that will blow the takeoff warning horn to resume taxi. Years ago the common remedy was to pull the takeoff warning horn circuit breaker. Inevitably, the breaker would be forgotten, sometimes with disastrous results.
Here's one example:
http://www.flight255memorial.com/thecrash.html