Lots of wives would be okay with this! It isn’t a betrayal of trust, it’s not an open-ended arrangement with unknown scope and terrors, it’s plainly declared up front, it’s so infrequent that it has little to no risk of displacing the primary marriage relationship, it minimizes jealousy, it isn’t a side fling that could be stumbled across by accident in the everyday by the wife, it’s a controlled outlet for long-term desires, it’s not likely to cause financial distraction, dependency, or drain. And that’s just ninety seconds worth of solid good reasons :)

I can explain it.

There is something in it for the wife. The world is a bit more "House of Cards" than some people assume. Aside from the French and a few others, western cultures seem almost uniquely dishonest about the tacit assumption that successful men will have mistresses. This isn't a new thing. Warren Buffett was essentially married to two women most of his life and no one cared.

Many wives highly value the accrued status of being formally married to a high-status person. You can take half the money but the social status doesn't follow. No one cares about a billionaire divorcee with no status beyond a bank account.

Billions, remember?