I've had many many bikes over the years (almost 30 now?

) with varying degrees of toe overlap. I've learned it's not a binary thing: you have it or you don't. Instead I see it as a gradient: a little toe overlap, a little more, or a lot?
If my toe just brushes the tire at the closest point, and overlaps, say, a quarter inch or so, it's usually no big deal and I have few problems.
On the other hand if I have a good inch or more overlap, then it's harder to live with. I had a bike like that and the difference isn't only in the overlap distance - it's also in the arc length (of my pedal stroke) during which interference is possible: it's a longer arc when there's more overlap. So I found interference during a bigger portion of my pedal stroke; my shoe spends more time in the "overlap zone" each pedal stroke. This means I spend more time overlapped and potentially unable to correct my steering.
Nevertheless I never crashed on that bike; it was just more annoying (and occasionally scary!).
Naturally there are in-between bikes too.