Yeah, there are certainly ways of preparing eggs that aren’t allowed in 24-hour diners (no line cook is doing “Scotched” egg next to your bacon), but poached or boiled are both allowed most places, on top of the normal fried options (sunny-side, over-easy, over-medium, over-hard) and scrambled.
Is this a joke? Fried eggs aren’t poached eggs and all you need to poach an egg is a pan and some water.
Yeah, there are certainly ways of preparing eggs that aren’t allowed in 24-hour diners (no line cook is doing “Scotched” egg next to your bacon), but poached or boiled are both allowed most places, on top of the normal fried options (sunny-side, over-easy, over-medium, over-hard) and scrambled.