Birds have feathers. And birds fly. But the feathers are not to aid flight. And I’ll prove it.
Dinosaurs evolved from reptiles. And birds evolved from dinosaurs (theropods). After all that evolution, much is still similar. Birds still have beaks and make nests and lay eggs in them. But birds and theropods have a new body shape (their legs that go straight down from their bodies), feathers, skin, and they lay hard eggs.
Compare photos of a chicken and a veliciraptor. Then compare their skeletons. There is not much difference at all. It is like comparing prehistoric and modern crocodiles.
The flying animals in dinosaur times did not even have feathers, but the flightless therapods did. And most modern flying animals do not have feathers.
Some birds have evolved feathers with special aerodynamic properties. But then bats have evolved skin, and insects have evolved wing-tissue with the similar properties.
Birds also evolved special bone structure to aid flight. Saying feathers are for flight is like saying bones are for flight.
Theropods evolved feathers, but they did that millions of years before they started flying. Many of them never evolved to fly at all, including many extinct dinosaurs and many living birds. The ability to fly is distinct from the bearing of feathers. There is no connection at all.
Can a bird with no feathers fly?
Probably not. Clipping a birds wings is commonly done to stop them flying. The feathers form part of the aerodynamic surface.
But bats fly without wings. They just use their arms a different way that doesn’t require feathers.
If having feathers removed can make flying impossible then the ability to fly cannot be entirely distinct from feathers (only condionally distinct). Sometimes flying is possible without feathers, and sometimes it directly depends on them. Or put in other terms, if you’re not a bird, you don’t need feathers to fly. If you are a bird, you will only be able to fly if you have feathers.
Bat wings have the exact same anotomical origin as birds (ie forelegs stretched out). If birds have wings, so do bats.
You are right. This is a better way of thinking about it.