As for the shitstorm, yes, they get used to your rule and calm down. But that was my point: lots of folks overreact and create the vicious cycle. Your kid complains, you give the phone, they shut up. Repeat. Repeat again. Now your kid expects the phone. And now you believe they will only ever stay calm if you give them the phone.
Breaking the cycle requires you to stick to your statements, but also, in public, to not give a shit about embarrassment. When you worry if you're disturbing everyone else or you feel inadequate as a part that can't calm a kid, you might give in. You can't!
PS: multiplayer games in my statement -> multi-player with me. Not internet.