For instance (and maybe this is embarrassing ...), I was late to the airport because the day before I went a bit later to bed than planned, so I overslept my alarm a bit, but still had plenty of breathing room. So I proceed, with the car. As it happens, I live in a country, let's say NL, and the airport was in BE. It also happens that fuel is significantly cheaper in BE than in NL (over 25% cheaper at the time). I'm also quite precise about fuel consumption.
As it happens, speed limit in NL is 100km/h during the day, but 130 during the night. I was still well within the high speed section during those very early moments of dawn. But I normally only ride my car during the day. So I know intimately how much fuel I'm using. So I calculate things ,with a lot of safety margins, to optimize fueling costs, by reaching BE with not a lot of fuel. However, as I was a bit underslept. Normally I know exactly how many km I can do after the low fuel indicator comes on. I of course anticipated this would be lower at 130/h rather than 100/h, but somehow, my calculations were a bit off. I ran out of fuel on the highway, well inside BE, but some 2km short of the gas station.
Not the best of times, as you can imagine. I was starting to panic a bit, thinking of eventual costs, I don't know the exact law in BE, if I have to pay someone to tow me, it would cost probably hundreds of time more than the potential savings. But somehow, the place where the car stopped was in a location under a bridge, where I could actually get off the emergency lane, so in a very protected spot. Must have been 5AM at the time, I proceed to walk towards the first exit, grabbing a plastic bottle from the ground. After about 800m i manage to get off the highway, to that first settlement, and not long after, a very nice gentlemen takes me to the gas station. I discovered, stupefied, that the station only sells truck diesel. I walk a few minutes to the next one. Same story. I keep walking until I finally find one selling petrol, and a very nice lady, after explaining her my situation, agrees to take me to my car on the highway, which was 1-2km away. I do pay her for her trouble.
Now, this whole incident only took about an hour, so I'm still sort of on track. But now it's starting to be early morning, and some of the worst traffic jams I've encountered. Basically the trip takes over 90 minutes more than originally estimated. I buy another plane ticket for another plane later that day and still end up not that badly, but ... yeah.
And also, if we have a very long margin of time, then does the 0.01% you might be late somewhere really justify something like this.
Obviously it depends on the context, but personally, things just happen in life and its hard to take into factor how many things are and are not in my control.
But from my perspective, the added example story was somewhat in your control. You just optimized for the wrong things. Of course this is easier in hindsight too.
Had you not run out of fuel, would you have missed the traffic too?
My fuel tank is always full. I fill it when it gets about 1/2 empty so that I am not caught stranded because I never know what will happen. Sometimes I get fuel even though I can make it, because what if something goes wrong? Habits die hard. I have seen highways close for hours to days after an accident or snow storm. If you're stuck there is no where to go.
And yes, everything is under our control and nothing is. It's a matter of perspective. Everyone prioritizes, since we have limited time. We choose what we do with that time. Just that, some people, sometimes me included, have such a time debt that sucks their time that it spills into their "obligations".
As for optimizing for the wrong things, this is also to some degree outside control. I obviously realize on a rational level why it's "suboptimal", penny-wise and pound foolish. But change requires effort and time. Which are sometimes used up in other more urgent endeavours.
You appear to be past the point where it's beneficial, and should focus on reducing it to improve your life. Granted this is easily stated when I have no real context.
Same thing happens to my partner. They're just fundamentally bad at estimating time and constantly do things that maximize their probability of being late.
Your story for example, almost nothing was outside your control.