I say it because it happened at my previous company: After a new team member joined the company (he was like 6, 7 feet away from me), I from time to time started getting weird smells, but it was occasional and it’s not like I was out on a hunt for the origin of the smell. Eventually we had to work together and wow, the smell was really intense (not sure if only that day or what); I immediately told him about it (it was just the two of us). He started using deodorant (that was the reason) more often after that. Weeks after I was drinking with his team, and they started talking about him and how much he had improved his issue, and I asked them if they had told them. They said no, with the reasons I mentioned above.
So, yes, people is different and you have to hopefully measure a bit what you say depending on the person in front of you, but if society wasn’t so sensitive these last years, it’d be easier for everyone to accept criticism so everyone improves. Also, if it’s something that directly affects me, there is NO way I’m not going to try and change/improve the situation.
There usually are repercussions, with concrete effects on work relationships and productivity (if there aren’t, why even bother ?). In your example, I’d guess people would delay talking to him and this would slow down communication. Keeping these kind of stuff silent usually don’t last long anyway, and it’s so much better to have early enough factual conversations, “we want you to fix X because otherwise it causes Y”, soon enough for the employee to have time left to digest the info and react on it.
If you genuinely think the ones you saw could have been avoid just by a conversation, I’d wager the main issue was not an awkward situation but a crucial lack of trust, often coming from a toxic culture.
I saw a lot of situations where something awkward was going in, ranging from bad hygiene to mild harassment.
Dozens of people are witnessing the situation every single day, even if the manager doesn’t step in there’s a flurry of other people with enough power or influence to intervene. That often means that the situation goes on because nobody gives a crap, or the one in fault thinks (right or wrong) that nothing will happen if the warnings/requests are ignored.
That’s just a crappy place to work either way. Quitting won’t be because of the awkward situation, but because it was a symptom of a deeper issue.