I’ve experienced very deep, fulfilling connections with strangers (friend of a friend level) and still haven’t found anyone being embarrassed by these questions, but of course nobody else needs to be around as it can quickly be embarrassing. It can also be softened with an honest “if you don’t want to answer I can totally understand” and move on with something else but almost always received a somewhat interesting response. In return, deep/very personal questions are sent my way and I’ve answered them all with the best of my knowledge.
I can see how many people are afraid of having real talk (specially introverts, as I was) because it can show your weaknesses, suffering and your potentially “wrong” ideas/thoughts. Truth is, everybody has their fair share of bs going on and being over polite and wasting time in meaningless small talk doesn’t IMHO benefit anybody, and you miss very interesting mindsets and experiences that can make your life much better.