Yeah I don’t see much from this notation (I also find it hard to tell the difference between the result of an abstraction and an application which feels like a somewhat important difference). I mostly wanted to suggest that diagrams or notation changes in general can be very useful.
It’s true that variable renaming comes up in other parts of mathematics but scope matters a lot less in most other mathematics, so much so that it is basically implicit and left to be inferred based on the mathematical context. You wouldn’t normally rename a variable to avoid a conflict so much as you would avoid giving it a conflicting name in the first place. The recursive nature of the lambda calculus means you can’t avoid the problem this way.
It’s true that variable renaming comes up in other parts of mathematics but scope matters a lot less in most other mathematics, so much so that it is basically implicit and left to be inferred based on the mathematical context. You wouldn’t normally rename a variable to avoid a conflict so much as you would avoid giving it a conflicting name in the first place. The recursive nature of the lambda calculus means you can’t avoid the problem this way.