There might be situations where people don’t. If they are young, if they don’t drive a lot, if they share their car, but most people keep them together, especially people who drive regularly, which Henry does because that is his job.
I’m wondering where you got the data from to make the assertion that you used to justify the harsh criticism of that scene’s writing. If “keys together” is just the way that you prefer to keep them, then I don’t think criticism of that scene is justified.