It's absolutely not best effort that counts.
I've heard many stories of people overstaying their visa in the US by e.g. one day, by way of a mishap or honest mistake, and subsequentially being denied visas or turned away at border control. The effects of this can go on for years and years... it's basically zero tolerance
I overstayed my visa by a week in Thailand couple of decades ago because the task I was sent out to perform took longer than expected. I just had to pay a reasonable fine on exit that I then claimed back on my expenses. There was certainly not even a suggestion that I would be unwelcome in Thailand in the future.
Why is the US so awkward?
Overstaying in the US
Anywhere else, less strict. Still can be problematic yes. And of course depends on the circumstances