You can get on a $500 plane ride to Costa Rica tonight, hostels are from $12 per night and quite fun. There's your serendipity. Just do it.
Not in the US.
https://www.bls.gov/opub/ted/2017/mobile/73-percent-of-all-c...
That is to say that time off will pay off in increased productivity.
Another way to say it, insufficient rest has its own cost.
To each their own but seeing travel, or even a short non-work break of some sort, in purely economic value might not be the most healthy outlook.
Who knows -- if you were to take even a one week trip somewhere else maybe the time away from your work will give you better insight into it, or even better thoughts/ideas, that might lead to more money / economic power, if that's your goal.