“Don’t make me horny. You wouldn’t like me when I’m horny.”
Or, in the case of the current series for The Flash, he can deploy them just after being punched in the face. They’re justifying him not being killed by all these normal people shooting him by saying that he heals really fast.
Remember, when “the other guy” spat out the bullet, it was Banner himself pulling the trigger. You might still be able to kill him if you caught him by surprise, but it’s tough to surprise yourself.
On a related note, why did he tell Scarlet Witch he could choke a bitch without changing color? The implication was that he was super angry with her, but it actually doesn’t make sense. Was it just hyperbole?
And when Black Widow tells Banner “don’t change” when they are fighting Ultron in the Stark building, he says he won’t.
My take is that Hulk is analogous to a temper tantrum (like putting your fist through a wall). Banner can be really angry and pissed off all the time, but if he stays calm and counts to ten or whatever, he can resist the change. If Banner looses his shit or faces a life or death situation, he Hulks out.
I think the point is that Banner doesn’t become the Hulk when he gets angry. He becomes the Hulk when he loses control of his anger. It’s the difference between being mad at somebody who’s annoying you and punching them in the face.
Bruce Banner was a victim of child abuse by his father (Incredible Hulk Vol 1 312 | Marvel Database | Fandom) which led him to fits of rage as an adult.