What impact does the paid vacation leave have on labor productivity? I'm asking just one question (it's in bold). If you treat any sentence with a question mark as another question and thus violating the policy on &quot;focusedness&quot;, please steer clear of the text below the sentence in bold.
What impact does the paid vacation leave have on labor productivity? Do employees get re-energized and work better, or is there no such effect (or is it outweighed by 160 or whatever lost working hours)? Are there any studies on that, what are their conclusions? Are American employers stupid or, on the contrary, prudent when they show reluctance to grant such leaves to their employees in the absence of employee-oriented labor laws in the US? Note, I'm not asking whether there is any positive effect of paid vacation leaves generally (on mental health, reported happiness, etc.).
What impact does the paid vacation leave have on labor productivity? Do employees get re-energized and work better...

There are not many studies that examine this question directly, but it is argued in the literature that based on the indirect evidence that shows that vacation does have health and happiness benefits on the employees that it increases productivity (Strauss-Blasche et al. 2005; Bellet et al. 2020).  Studies that examined directly various paid leaves from work generally find positive but not always significant effect of provision of paid leave/vacation on productivity (e.g. Bassanini &amp; Venn; 2008). Moreover, Zenger and Folkman (2015) provide some tentative evidence for increase in productivity from paid vacation that is also based on international comparison. However, the effect will also likely be heterogeneous across individuals, industries, time and place. One should not just assume just because the average treatment effect is positive the policy has the same effect everywhere every time.

Are American employers stupid or, on the contrary, prudent when they show reluctance to grant such leaves to their employees in the absence of employee-oriented labor laws in the US?

This question makes no sense. It is simply not possible to judge employers 'prudency' or 'stupidity' from their decisions to provide or not provide paid vacations and stupidity and prudence are not even opposites.

Prudence is defined as individuals proclivity to save more when faced with increased risk (Sandmo, 1970). Consequently, to the degree that there is any uncertainty about productivity gains from paid vacation a prudent employer would spend less on paid vacations not more.

Stupidity is not rigorously defined. If by stupid behavior you mean irrational behavior then game theory clearly shows that rational (and thus not stupid) behavior can often lead to failure of getting maximum possible payoff or profit in a strategic interaction like in a classic prisoner dilemma where fully rational actors typically end up play strategies offering much lower payoff than possible (See Tadelis Game Theory: An Introduction pp 48).

Increase labor productivity does not automatically means there is increase profitability. Labor productivity is defined as value of output over labor inputs. This does not take into account the costs that employer has to undertake to achieve this increased productivity. However, even if paid vacation would be directly and unambiguously linked to increased profitability, it is not possible to make any conclusions on whether employer is 'stupid' or 'prudent' for above mentioned reasons.

Amount of paid vacation days is part of total compensation. As such it is negotiated over by both employee and employers. A poll among American workers showed that significant amount of them do not fully use all their paid vacation days. Consequently, this provides at least some evidence that in the US workers are not interested in paid vacations. Hence, a rational employer would minimize provision of benefit that their employees do not want, and maximize provision of work benefits they do want, because benefits (provided they are wanted) are substitutes for higher wages. It would be irrational to provide benefit a worker does not want since then employer has to still pay for high wage in addition to unwanted benefit (see Borjas Labor Economics 223-224).