I use a case and I have (very rarely) dropped my phones, but I’ve never broken one (or even significantly damaged one) by doing so. I suspect that might be because the lip of most cases protects the screen from direct impact with flat surfaces. Or maybe I’ve just been lucky.

And I do agree with you that a case bulks up the phone a bit and you lose that satisfying thinness. However, to me, there’s a positive trade-off: if you get the right case (like a silicone one), you can significantly increase the tackiness of its surfaces, giving you a much better grip on it. This, to me, is the chief benefit of having a case—not to protect it should you drop it, but to make it so you’re much less likely to drop it in the first place.