Why did Birds Lose their Teeth?

Every living bird has a beak and weather they are being used for foraging, killing or attracting a mate their bill is paramount for their survival. However, this definitely wasn't always the case and many millions of years ago nearly all of them had a row of sharp teeth instead. However, strangely birds weren't just toothed at some point and actually they had teeth for a large part of their existence. Whereas their other defining features like their feathers and wings have been around since the beginning. So their bill is not as important to what it means to be a bird as much as you may think as they got on fine without them for an incredibly long time. so why are all birds alive today Beaked?

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Sources:
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https://www.nature.com/articles/natur...
https://www.researchgate.net/publicat...
https://www.nature.com/articles/ncomm...
https://www.nature.com/articles/s4146...
https://www.researchgate.net/publicat...