I have never had a hot dog fall out of a side cut bun. Every time I've used a top cut bun I've felt like it was going to fall out, and it has on at least one occasion that I can remember - and it's not like I remember the details of eating foodstuffs.

The side cut gives you easy gripping surfaces. The undisturbed tops and bottoms of hot dog buns are easy to grip. The sides are inherently less structurally sound because they're "inside" portions and spongy, and when you grip them you're likely to grip the bun very well but apply pressure to the hot dog itself from direct points at your fingers rather than the bun distributing the pressure evenly through the structure.

Gripping a top-cut hot dog bun is like squeezing a baseball half in a mitt - The ball just pops right out the front, and so does the dog. It launches straight upwards and then falls where it may.

I don't have a fundamental issue with top cut buns, it's just the ones I've had aren't cut deep enough to fit Italian sausage and all the fixings. But if you want better bread that's the price you pay.

I'm not American so maybe my question will sound silly but folks, what is wrong with picking a knife and cutting your bread yourselves exactly the way and depth you like?

It can be a tough call on whether the bun will stay in one piece if you try to cut it any further! Bun splitting is tragic, and I would rather cram toppings to stay on the safe side than risk such a fate.

If nothing else, hot dogs are popular in finger food settings where utensils (especially knives) may not be available.