1. Jet engines need very little (seconds) warming up except where there are specific issues like engine hydraulics whose fluids and seals may need to be warmed in very low ambient temps. Piston engines need to be warmed up for two basic reasons. Firstly to bring the pistons, rings and cylinders to a stable design temperature so that the various fits and clearances have closed to the intended design values, risking gas blow-by and consequent damage to the rings and cylinder bores if run at more than minimal power. Secondly it is to warm the lubricant to within its intended operating range - when too cold the oils won't "wet" properly and so lubrication is poor, risking metal-to-metal contact (and subsequent engine damage/failure) if run at more than minimal power. In the case of liquid-cooled engines it is also necessary to bring the coolant to working temperature to avoid the risks of shock-cooling parts of the block and heads with cold coolant.
2. It would definitely be a bad idea to have lots of tug vehicles mixing with aeroplanes on taxiways and runways. The risk of collisions would be unacceptably high for an un-necessary risk. Fuel consumption whilst taxiing and holding is often reduced by only using one engine, starting the other(s) just before final take-off checks (depends on the aeroplane, the operator's procedures and the ambient conditions - single engine taxiing in high winds and/or on a slippery runway is generally avoided). This rather proves the point about rapid warm-up times for jet engines.
The amount of fuel used in taxiing and holding is generally negligible compared to the amount used at cruise power, so it's not THAT big an issue.
3. "Shore Power" is fine where the services required are electrically driven. Cabin conditioning usually isn't. There's also the detail that it would need to be metered and billed, which just adds more administrative bumph which would be difficult to justify when the aeroplanes all have perfectly good APUs. Also who pays the bill if "bad" shore power damages an aeroplane? How would you prove it?
Last edited by PDR1; 28th Dec 2016 at 08:40.
Reason: Edited to answer shore-power question