Haven't read the entire thread so don't know if already mentioned, but:
If it matters to you that your children's school has a good OFSTED rating, then timekeeping matters very much to them.
If your school has a 'problem' with lates or unauthorised absence, it will be noted ,without a doubt, at inspection and the school will be expected to do something about it.
You may not care less about being late, but plenty of other people do, and manage to get to school on time.
Besides,what message does it send your kids if you are habitually late? That its ok to be late for appointments? Work?
If you are late for a train or bus, it goes ahead without you. Much like school.