I wasn't addressing a few days off at Apple, but your comments about longer PTO and productivity in Europe. No one said anything about nose to the grindstone / burnout as the alternative, which is obvious.
imo both of you are oversimplifying
consider these two stereotypical examples:
(1) blue-collar worker in some factory
- hired to work 40h/week
- after his shift ends he goes home and spends some quality time with family
- if he is slow he gets fired as the time budget he
can work is fixed and determined by shift schedules etc
- works overtime (or weekends) when told to do so and gets compensated for it
- if he is late to work, goes early, ... he needs a replacement to take his place, if there is no replacement tough luck
- you give him PTO and his annual output goes down proportionally
(2) junior consultant at a major consulting firm
- employment contract says 40h/week
- after "work" he spends a few hours writing up the day's results, then takes a shower and spends 3-4 hours socializing with the client, when he gets back to his hotel room late at night he puts in another few hours to rework his slides for the next day's presentation
- if he is slow he just works more overtime until he breaks down; then the quality of his work will suffer and he gets fired.
- if there is a legal obligation to keep track of overtime everybody reports fake values, nobody wants to red-flag himself; overtime work is done from home whenever possible for the same reasons
- nobody cares when or how long he works as long as he shows up for meetings and is there when the client needs him; taking a few hours off to pick up his daughter is generally no issue.
- you give him PTO and he will probably spend most of that time working from home; in any case he will be back on his original schedule by next week.
Most jobs are somewhere on a continuum between these two extremes, the exact position is usually determined by company culture and pay-grade.
But 3 days PTO does usually not imply that all project deadlines are shifted by 3 days.