Surely it's intended as a more deliberate (not technical) device - seeing his 'reflection' we're seeing him as he sees himself, his self-image. (I haven't seen the film though.)

Oh, I understand the cinematic effect, what I'm asking is why they used a trick instead of an actual mirror. I suppose because the actual mirror would have shown the camera behind, right?

Even for a momentary shot of a doorknob in ‘The Matrix’, the camera had to be hidden—in the jacket: https://collider.com/wp-content/uploads/2019/05/matrix-doork...

Very cool! I didn't know that. It's amazing all the kinds of shots that are done in movies that one would assume are trivial to accomplish, but that actually require tricks.

You are correct!

Without using this technique you'd have the camera in shot.

I don't think it would work with an actual mirror - either Cassel will block the mirror or the camera will block Cassel.