It's similar to how the economy benefits from paying workers a decent wage.

Due to many different reasons (including fear of revolutions), western countries decided it was preferable to pay workers a minimum wage. To the elite's surprise, it had an additional benefit to them. It turns out that workers spent the extra money on maybe eating meat once a week or buying an extra pair of pants. Later they even had a name for it: "Disposable income". Yes, the factory owner had to pay more wages, but they also increased the potential customer base.

I think these rooms have a similar benefit to society that is hard to measure directly. There are many stories of "third places" that leads to lower crime levels, lower unemployment etc.