Over the years I've been surprised how often people are chronically late for their obligations and the weakness of their excuses. If you're a genius and people don't care if you're on time because you're the best at what you do that's fantastic. Most of us, however, deal with the reality of external obligations like deadlines and teammate expectations.
Creativity is fueled by constraints. Most working creatives apply both personal and external constraints. Personally I've known creative geniuses who can't work within the framework of outside rules and I've known geniuses who thrive on external expectations. The question is whether a person can only work within their personal constraints or can they adopt another system? Whether we're geniuses or not, most of us have to collaborate with other humans and it's reasonable to expect that we share some ground rules to keep things running smoothly. And if someone is paying you to make something you can bet they'll expect you to be on time.
In most cases being late is your fault. You can easily check the traffic online or on your phone and plan accordingly. Ditto for the subway. Your alarm clock didn't go off? Weak. You forgot something at home and had to go back? Your fault. When you blame an outside circumstance you're really saying, in effect, that you're not able to plan in advance or manage your time. Your cat got sick? Some other disaster slowed you down? Okay, things happen, but you only get to use those catastrophes once. Bundle them with a history of lateness and you aren't reliable. And trust is the key thing here. If you're employer can't trust you to arrive on time they won't trust you with other responsibilities. To be clear, your lateness will limit your opportunities. You may not lose your job but you should expect chronic lateness to affect your potential for responsibility, raises, promotions, etc. How you do anything is how you do everything.
Your lateness doesn't just affect you. If you're late for a meeting it affects everyone at that meeting. Add up the loss of time and money from people waiting for you, or recovering from your late arrival, and you can easily put a price on your unreliability. You screw over a manager or a team-member every time they need to scramble to cover for you and it's a clear message that their time is worth less than yours.
Managers pay attention. Your employees take note every time you're late and they'll follow your example. If you don't respect them enough to be punctual why should they be on time for you? It doesn't matter if you're the one signing the paychecks because respect goes both ways.