I was always driven mad by my mother's attempts to shrink time. She commuted to London and every single morning assured me that the walk to the station took seven and a half minutes, tops. However, even the fastest walker in the land couldn't realistically, have made the journey in less than 10 minutes. She was also a great one for being "absolutely ready" to leave the house. This, in reality meaning "after I've made, poured and drunk an entire pot of tea, fed the dogs, changed handbags and generally found it impossible to walk straight from kitchen to front door and out the other side".
I also find it incredibly insulting when the late person has the gall to say, for example, that they were having a lazy morning. An airy sort of non-excuse that is intended to make you come across as neurotic about time-keeping.
But I do think there are some people who are genuinely deluded about what can be fitted into a certain time frame. DP's ex-wife would, at very nearly the time they were due to leave the house, suddenly decide to bake a cake or finish wallpapering the kitchen.
This said, I'm not very bothered by anyone arriving 10-15 minutes later than arranged since I do think that "3'ish", say, is a perfectly acceptable concept. But I do expect people to recognise that there's only 15 minutes to an "ish" (tops).
On the other hand, and having suffered from this for many tiresome years, can I just say that arriving repeatedly early is also very poor timekeeping and is definitely not a virtue. I have a friend who really couldn't (and still cannot) understand that 3'ish means 3 o'clock onwards. It does not mean fetching up at 2.15 and wondering why you aren't ready or that it is hugely inconvenient to have her following you around the house hindering you even further.