as i said if you want infinite dimensional things like Fourier transforms acting on function spaces you may benefit from additional abstraction. but even those people will benefit from having learned Rn first.

i’m as much with bourbaki as the next guy. but that’s not really how most engineers learn in practice.

as for treating linear maps between finite dimensional spaces as vectors that’s quite straightforward to do in coordinate terms.

again i refer you to the classics like Golub and van Lean that have been reprinted many many times and educated generations.