i think most people just aren't equipped with enough empathy to respond reassuringly, if at all.
I would go a bit further with this.
Personally, I am very much equipped to respond to the topic of suicidality as I've been living this hell for most of my life and can relate to and empathize with it all day long.
However. To engage someone about this requires a certain mindset. If we're just having a light, casual conversation, and you suddenly tell me about how you were thinking about killing yourself last night... That is a shell-shock "whoa" moment that is apt to stupefy even the most seasoned professionals. There is a process of reorientation that has to happen in order to make that transition from "light chatter" to the "deep and dark".
I think, in the moment, it would actually affect my ability to respond in a way that I'd want to respond. So much so that I might
seem uncaring in the moment. And my thinking on this is, if this "casual drop" would catch ME off guard, then just imagine what it would do to the average person who has no personal experience with it.
Being so accustomed to suicidality, I have to be careful in my everyday life to avoid accidentally let something slip in a flippant manner. Yes, it's casual for us, but not for the average person, and for some people, you could shake the very foundation of their world by dropping this information at all, let alone catching them off guard with it.