The other day I had a conversation with a co-worker ("user" in IT speak). We started talking during my lunch break but I hadn't looked at the clock. After a while I started to get a little anxious about the time...was my break almost over? After a while, I decided that it didn't matter and committed myself to the conversation. Lunch went a half-hour over but I relaxed and was a much better participant in the conversation.
When I was in college I took a cultural anthropology class because, hey, a guy's gotta fill requirements. Right?
The professor pointed out the different ways that cultures think about time. We western folks are very linear and regimented. Work starts at 0800, lunch is at 1200, day ends at 1700, and so on. Some other cultures take a more circuitous view where time is more relative.
The instructor's example was like this: Someone from a western culture might meet a friend while walking to work, stop to talk but cut the conversation off after looking at their watch and finding they're not on schedule to arrive on time. Other cultures would find that offensive and would take as much time as necessary to finish the conversation before continuing on their way. Time isn't as important as the person.
We often don't value people as much as we ought to. Relationships are important. Being a part of the organization is important. We use metrics and frameworks to make workers and processes as efficient as possible but people aren't machines, yet. Yes, timeliness is still important and we can't simply change ourselves and our workplaces into an anything-goes sort of schedule. As with most things in life, there's certainly a middle ground we can achieve.