My mum has always been pretty laissez-faire about time and work. She always runs late, but at the same time, she put 100% effort into the job. She never misses a patient, barely has any time to eat or pee when working, has to drive around all over the county to different GP surgeries, and stays late to write notes up.
She will stay as long as it takes when, for example, a patient is suicidal and needs urgent referrals for their own safety, she will work at the weekend if there is a backlog of work, and she is generally well thought of and respected as being very good at her job. Whilst she might be late for admin times/group meetings, she is always there for a patient (half of which never turn up).
There are definitely jobs where punctuality is vital, time sensitive work, retail work, customer facing work, etc. But I think there are definitely careers where so long as work is done in an appropriate manner, that it doesn't really matter if someone is late in the mornings, and takes time out to greet colleagues and get themselves a drink.
I guess it depends on whether someone is depending on you to be at a certain place, at a certain time or whether there is time to spare that can be made up, either by working extra hard or by staying a bit later to make up the time missed first thing. I know I'd prefer a career like the latter where time management is something I am responsible for, rather than being told where to be by a manager and facing sanctions if I am not there.