You've fallen into the trap of reading about something that is written by someone who has no real boss and thinking that you could apply it to yourself.
Living 'without time' is a great idea and is ideal for how we, as humans, have developed. Unfortunately, in the real world, the rest of us need to use time to make sure we do things on other peoples schedules. Whether it be the boss, the airline, the doctor, the kid's school or whatever, we need to make sure we're aligned.
You will only be able to really do this if none of those things apply to you and you can spend your days doing whatever you want.
Whilst there is a lot of truth here, as a founder I can say it's still very easy to "do things on other people's schedules". I think there is still a lot of discipline required to experiment with something like this, even if Steve has no "real boss".
Let me put it like this. I have enough problems with being late as it is. (Mind you, I think probably in the median when it comes to lateness issues among my friends.) No doubt this is indeed a source of stress in my life.
I fail to see how eliminating clocks from my life could possibly make this situation better. If appointment reminders plus clocks don't get me there in time, appointment reminders alone aren't going to do it.
I suppose I could adopt a policy of not caring if I am late, but in general that seems incredibly rude.