Fuel saving would be only one of the benefits.
Airlines would also significantly reduce engine operating hours, reducing engine wear and thus maintenance costs. I’ve been on flights out of Heathrow that seem to spend almost as much time taxiing as they do in the air (due to weather or ATC delays or whatever), so for short-haul operations this seems really significant.
Local air quality is also a concern for airports: the air in the neighbourhoods around Heathrow often stinks of jet exhaust, sometimes you can smell it from miles away. Presumably, much of those emissions come from taxiing aircraft.
The limiting factor for most turbine engines isn’t really operating hours, but “cycles”, which is to say starts and stops. From a maintenance perspective it’s not terribly important whether you start the engine at the gate or the runway.
Also, as far as maintenance goes, engine hours are weighted by operating power. So, an hour at idle doesn’t count as much as an hour at cruise power. One of the reasons airlines started using not-full power on takeoff when conditions allow it is because of “power by the hour” maintenance contracts, which incentivize that.