There's best practices which is what the lawyers want to say for CYA, and then there's real world where the equipment gets used and abused.
In the manual for my generator it says to disconnect load before shutting down. Well, sometimes I remember to do this, sometimes not. As far as connecting after starting, well, my transfer switch takes care of that. It doesn't connect the house circuit to the generator until after it "validates" that shore power is clean and stable.
Warming up for "a few minutes" sounds excessive. If it's very cold I will let my Yamahas warm up maybe 30 seconds before connecting. It's not running a large displacement diesel engine, what does it need to "warm up" exactly?