Vacations Are Essential!
From the First Lady’s perspective, I'd say that 16 vacations (many of them 3-4 day trips) in three years is quite reasonable, even conservative, especially for a family of means living far from extended family. It's not like they're getting a ton of extra quality family time at home (aka Daddy's office).
Vacations are an important part of employee wellbeing. They allow workers to recharge and relax, to get away from work and clear their minds. Workers return refreshed and ready to go, with their creative juices flowing. (This assumes you actually allow – and require – your workers to separate from work while they are away.)
Encourage a culture that allows (encourages) regular vacation use. Consider mandatory minimums for vacation or random company-wide days-off to allow everyone some breathing room without feeling like they have to work overtime to catch up when they get back.