Dude, you literally scan left to right on most systems. This is not a point of discussion and it's not remotely difficult.

On Windows, I don’t stop to think “hmm, which edit menu is this”. And, if I have multiple windows from the same application open (multiple document interface), I know which document the edit menu is for.

There is a genuine tradeoff here. Global menu bars are easier targets and waste less space. Per-window menu bars are more clearly bound to their window. Neither approach is better on all counts.