Politics aside, they say President Clinton (and this may have to be updated in a couple of years to be clear about which one) was always late to appointments, whereas President George W. Bush was always impeccably on time. The speculation went that Clinton made people wait to show them who the 'big dog' was, who had the most power. It was a message.
But what sort of message does being chronically late send?
It's not that there doesn't exist such a thing as being "fashionably late." (Although it doesn't have as much to do with fashion as it does with politeness.) The assumption (and it's a good one—of course, depending on the circumstances) is that your host or the person you're meeting might not be ready. It's a courtesy, a grace period, in which your minor lateness is saying: "Just in case you're not ready, I'm going to be just a few minutes late." It's a nice thing to do.
Whereas as to be chronically late for long periods of time is something very different.
Returning to President Clinton's example. His lateness is saying: 'I have a higher rank than you, so you are going to wait for me, and that waiting is going to make it perfectly clear who has more power.' And perhaps it's effective in conveying that message. But it also conveys much more.
It conveys low self-esteem. It says: 'I'm so insecure that I feel I have to assert my dominance via the rudeness of being late.' It says poor manners. It conveys a lack of respect.
Whereas being on time conveys just the opposite. Being on time says: "Your time (and you) is just as valuable as mine." It conveys high self-esteem. In the sense of not being afraid to be on time (afraid because of buying into the neurotic perspective of 'he who is late has the power'). And it reinforces self-esteem, because self-esteem is reinforced by doing what you say you're going to do. (Including meeting someone when you say you're going to meet them.)
Other potential messages being late sends are: laziness, lack of intelligence, forgetfulness, hurtfulness (picture being late for your child's graduation or wedding or whatever is important to them). Whereas being on time conveys just the opposite: vitality, intelligence, an acute memory and kindliness.
If you want to show a person you respect, value and care about them, be on time.