We evaluated taxiing one one engine last year, with mixed results;
For the A320/321 fleet this became an approved procedure after landing only
, saving both fuel and brake wear, as the A320/321 have quite a lot of residual thrust at idle so braking is required with both engines running to keep the aircraft at a safe taxi speed.
For the B757/767 fleet it was rejected. The heavier weights of these aircraft meant that you need to apply a fair amount of thrust on the live engine break away from a standstill, and more thrust than normal to keep the plane moving, negating any other savings you might make. Also the GE
-CF6 on the B767 requires a 5 min reccomended cooldown period after landing before shutdown.
It was felt undesirable to delay engine startup on departure for any aircraft in the fleet. Starting all engines on pushback provides some degree of warmup, and also problems that can occur after startup may not always be apparent to the crew, and may not become so until the aircraft has commenced it's takeoff run. For example a fuel leak from within the engine would be reported by your pushback crew, but if you start that same engine at the holding point, there may well be nobody to see it...
Just one operator's experience.