All of my 2T bikes that I have owned in the last 30+ years have and will idle all day long. The logic of the bike idling for prolonged periods and not getting enough lubrication just doesnt make any sense. Here is my reasoning. If you have the jetting properly tuned and your running the correct pre mix ratio. You will always be getting the correct amount of lubrication in the cylinder to lubricate the cylinder walls and the wrist pin bearing and the lower crank bearing. Its all about the the jetting and the pre mix ratio. Now if your of the opinion that because of the type of riding that you do. Due to plug fouling or whatever. Youve elected to go from running say 32:1 to say 40:1. Then yes you could run into lubrication issues but that would be at every throttle position setting, not just idle. The engineers that designed your bike engine figure out that the proper premix ratio is supposed to be what ever it says in the manual for your bike. Be it 32:1, 40:1, 50:1, 60:1 or 100:1. Most common premix ratios for larger engine bikes like 250 2T bikes is 32:1. There are some exception. Like KTM they give you a range of 40:1 to 60:1. But they have engineered their engines to operate at those ratios.
So If your bike wont hold an idle whether its cold or up to temperature. Its probably your jetting, your airscrew adjustment, or idle screw position. It could be all three of those thing. It could be two of those things, or maybe just one of those thing. It could also be how fresh your top end is, if it wont hold an idle. Or even the condition of your cylinder. If the cylinder damaged or worn out it could cause the bike to not want to idle. Or if you reeds are worn out or damaged. That can cause the bike to be hard to start and hold an idle.
But yes your 2T machine can idle for prolonged periods.