It depends on the bike though. I mountain bike with large soft tires, good suspensions, and low air pressure have quite a lot of grip compared to a road bike with tiny super hard tires. You can do a lot of crazy things. But I agree that the average commuter bike has low limits.

"the first time you realize your bike can go from well behaved to on the pavement instantly is the worst time for it to happen."

I am always afraid of falling of the bike while there is a bus driving behind me. Could happed with a pothole, random garbage/bottle of the road, etv

If you’re an urban cyclist find a safe place like a parking lot to practice sudden braking, tight turns, etc. And if there’s a suitable spot practice riding on gravel too… Should roughly simulate loosing grip on rough roads.