sounds like it's drowning on fuel > O2 sensor, intake air temp sensor, something like that could be fubar which makes the ecu enrich the mixture.
as for the other stuff; after a cold start, only wait for the oil pressure to rise, then engage the clutch and drive off and stay below 2500/3000rpm untill your oil is at NOT. Letting your car idle untill it warms up is wasting fuel/time.
Engine wear ONLY occurs when there's no oil pressure, as soon as you have pressure the wear stops as there is an oil film between axle and bearing caps. The reason you should not rev high or put a big load on the cold engine is because the oil film protection/lubrication works on flow, not on pressure as is widely misunderstood. Ever noticed your pressure drops when oil warms up? So if lubrication would be about pressure, then you should be able to put a big load on your engine when it's still cold because you then have high oil pressure...
So no, it's about oil flow. When oil is cold it is thick and doesn't flow enough to lubricate the bearings when under stress > high revs/big load, cavitation can then occur and then you WILL have metal to metal contact which destroys bearings.
That is the main reason not putting stress on a cold engine. However, cruizin below 3000rpm is not putting any more stress on the engine then when you let it idle. The oil warms up more quickly when driving and also, your gear box oil warms up, which is not the case when you let it sit and idle.
Furthermore the quicker your engine warms up, the quicker it will leave the cold start enrichment dumping fuel into your engine and dilluting your oil.
It also has nothing to do with clearances getting into spec when warming up, at least not in our engines, it does play a role in ultra high performance engines like F1 and funny car drag monster engines, but not on our engines which are designed for daily use. There is enough clearance on our engines to never be an issue, remember toyota (and all other car manufactorers) tests cars and engines from polar to desert conditions and they should start and go in all these conditions, that's what it's designed for.
So, many reasons to only let the oil getting to pump around and start driving asap.
and btw, I like driving in the cold, MORE POWAH!!