I know people who *prefer* to bind as you described, and have never heard of it being an issue in real life.
I have *read* about straight-grain binding wearing more quickly than bias, but I have a suspicion it is a rumour concocted by the same people who recommend always cutting border joins on the diagonal 'because it makes them less obvious' (on rare occasions maybe, depending on the fabric pattern, but otherwise it just uses more fabric - so you have to buy more & spend more money)
So my answer would be: leave it as it is.
