A few points.
Most modern fuel injected (FI)engines do have a richer mixture at startup, but usually also have a higher cold idle speed, to warm-up quicker, it also helps move oil and fuel faster thru engine.
The problem of "over-choking" a cold engine or running and excessively rich mixture for too long we had with a manual chokes is not an issue anymore with FI. The computer controls all that and with ever increasing emissions requirements is calibrated to be as efficient as possible (Lean).
Warming up at idle or driving off after starting in most cases/temperatures were you would use scooter/ bike is ok.
A properly working lubrication system, using the specified oil type, etc.

, should extinguish the oil pressure light immediately or at most in a few seconds and circulate oil thru engine in less than 5 seconds, regardless of outside temperature, don't believe that, run any cold engine with the valve cover removed for 5 seconds, see what you get
