I always make a point of not moving after start, until the oil temperature is in the green.
I am wary of absolute rules in aviation. Like many things in aviation this is IMO one of those "it depends" things".
Lycomings direction is the engine is warm enough to fly if it will go to full power without stumbling. All of the small Lycomings will do that with no oil temp showing on the gauge.
I am certainly not criticizing your practice of waiting for oil temp to register before taxing and that is certainly a non optional practice for radial engines or any of the bigger turbo charged flat engines, however I see no problem with taxing any of the simple flat 4/6's a soon as the engine has stabilized after start
Again the oil is the key. Are you running multi grade or a thick single grade and how cold is it ? The oil pressure gauge will tell you were you are at in terms of when you can increase power.
The flying club where I used to teach had a bunch of C 172's. They ran them to 3500 hours between overhauls with no problems and I can guarantee with the hobbs running nobody waited until oil temp showed on the crappy Cessna gauge before taxiing.