When you are playing your Long tones, you need to have a certain amount of tension to ensure that you flute is not moving around while you play.
I do agree that playing an etude with a metronome is a good idea.
What ever you play, I hope you enjoy playing it as much as I have enjoyed playing all of these flutes over my career.
I think too much is spoken of playing things slowly.
Listening to all these really fine players play I was impressed that they all sounded good no matter what they were playing upon.
I have always bought modern flutes and enjoyed playing them.