Fuel conservation programs are leading to single engine taxi out, asking the crew to start the other engine near or on the position 2, where the ground crew cannot monitor the engine's status outside the aircraft. How safe is this procedure? One example is the jet pipe fire during the start up.
I am not aware of mechanics watching civil aircraft start up. They usually have far better things to do. Aircrew are responsible for the aircraft at this point.
The question on a twin is about directional control not safety. How easy is it to taxi on one engine without losing control or stressing the aircraft or tyres in any way? I think this probably depends on the aircraft, some will be easier than others. Also if its a piston twin, you don't want to wait for the other engine to warm up when you are ready for departure. Some four engined aircraft might taxi on two engines - one either side but I've never heard of twins doing this routinely.