Except that it usually isn't a net positive for the host country. The host country gets zero percent of the signage revenue, tv revenues, ticket sales, or merchandising revenue from the Olympics.

The only way the host country makes money from the Olympics is if tourists spend enough money on lodging, food, etc. That pipe dream hasn't worked out well for several countries who've recently hosted the games. The deal is so bad for the winter games that few countries are bidding it anymore.

There are similar parallels with professional sport leagues in the US. Maybe the whole thing is a combination of government officials looking for prestige, and a couple of mediocre economists rattling off numbers to back it up?

Absolutely. There are plenty of elected officials who want the prestige bestowed by hosting a big international event (e.g. Formula 1, World Cup, the Olympics), and I think many of them believe the idea that the potential tourism revenue justifies the expense. Many citizens fully believe the same thing.

It's only recently that more people are realizing that the numbers don't usually add up. Even then, lots of people are so passionate about sports that they simply don't care about how much public money is poured into a black hole to host these events (or build stadiums). And that's not even getting into the corruption.

What, like the London Olympics in 2012? Did that bring in £20+ billion? Funny - I didn't notice my taxes being reduced or anything; just a few weeks of roadworks and unpopular sports being shown on TV.

Mostly because £20 billion is about 4-5% of the budget in 2014 and that year there ware a deficit of £84 Billion.

If the infrastructure being built isn't disposable, then it makes a lot of sense. For example, building a new transit line to the airport would make a lot of sense.

Building a gigantic temporary stadium does not.