“Hi, How are you?”
“Well I woke up this morning and stepped on my dog’s tail by accident. He was not happy with me, but we’re all good now - how about you?”
Another reason, though, is to me one of the main benefits of social interaction in the first place: The brain rewiring also makes you think about what other people would think, want to hear, say to you, etc, even when they're not around. That sure can give you better answers in conversations, but more importantly, I think this is just genuinely a nice way for the brain to be. In the same way that dogs are happy playing fetch, humans are happy living with other people in mind. Maybe because it feels like not everything is your responsibility, or that you worry less about what you should be doing, or that you look forward to laughing about disasters later... I'm not entirely sure. Whatever it is, it's nicer than the alternative.
Alternately, instead of trying to prepare for every possible answer, you can constrain the possible replies significantly by being the one who asks the question in the first place. "How's your day going?" is only ever going to get some variation of "good" or "bad". You only need to respond with "great to hear that", or "sorrt to hear that, hope it improves soon". That's it.
Your suggestion would work when both people are in the same place for some time, e.g., waiting in line for a coffee, or for a meeting to start or for a lift (elevator) to arrive, etc.
I sometimes go to concerts by myself and like to arrive early to catch the support act. There’s usually a gap of at least half an hour before the main act comes on stage and I make a point of looking around for other people who aren’t on their phone so I can start a conversation. In that situation, I already know we have something in common.