Jabba,
In my experience the injected Lycomings I'm most familiar with have been much much easier to start cold than warm. It's almost impossible to stuff up a cold start but I've seen plenty of botched hot starts. There's one flying school not far from here who's students seem to have no end of bother with hot starts on their injected C172's. However like anything YMMV.
Also I have a lot of experience with pilots new to an aircraft and or fuel injection and they tend to be ham fisted with starts usually having too much throttle set The OP also mentioned high RPM at start up. That is why I consider having your hand on the throttle instead of the mixture is a much better idea.
If you're flying that aircraft all the time then you'll know exactly where to set the throttle but there's a lot who don't.
There is no need to be in a hurry to advance the mixture.
I agree there isn't generally a need to go full rich until you're ready to roll.