not all birds carry food to their young externally.

there is the sea bird that reguratates a slime (gelatious mess) that is the basis for 'birds nest soup'

pidgeons regurate 'pigdeon milk' for their young..

and other other birds that do the same thing.

some birds regurated food (basically undigested) from their crop, (which i supposes, technically is not quite regurated) others start to, or completely digest the food before regurating for their young.
(eagles and hawks often bring live (but with a broken back) prey to their nest, so the young can play with their food before they eat (as cats often do with animals they prey on!)