BA 75/76 we are encouraged to shut one down on taxi in to save fuel.
In practice it is only done when the stand is known, so which engine to shut down is known. In addition, most will not do so on E4 ac since the idle thrust is so low, 76 can also be difficult. However, a light C accelerates well on just one engine, so not only saving fuel, but also brakes...
As has been stated, some loss of flexibility if the taxi in plan alters...
NoD