> Why on earth would somebody who's interested in profit leave a property empty, rather than cash in on rent from tenants?

IANAL, but I did read once (apologies, can't find the citation), that depending on the ownership model, you can write down the cost of "no rent" on your tax bill. So if you have revenue from other sources other than property, it's not much of a hit to leave it empty and make the gains elsewhere in your portfolio.