I'm not directly privy to the operations of the IOC, but quite a bit of info is in the public view.

Host nations definitely spend a lot on the games, for the prestige of it all. In recent years, democratic nations have been less interested in hosting the games because it brings too much domestic tension for not enough international influence, although that's not to say they have no interest in it.

It's also not just about soft power itself though. If your country can run an Olympic games, that implies to the world that you're a stable country with infrastructure and resources to spare. That both signals that you're likely able to defend yourselves, and encourages international trade.

While the host nation spends a lot on the Games, they don't pay for everything. The IOC also pays for things. For instance, the IOC contributed over 1.5 billion USD to Rio 2016, just in terms of helping to actually host the event. That's excluding their own operations, own advertising, own broadcasting costs, and various other things like flying their own staff around. https://olympics.com/ioc/faq/roles-and-responsibilities-of-the-ioc-and-its-partners

On top of that, the IOC runs the Winter games and works with the IPC for the Paralympics, contributing a marketing budget there. They also contribute to scientific advancement I believe for anti-doping tech.

Of course, the Winter Olympics and Paralympics are nowhere near as marketable or commercially viable as the main games, but the IOC thinks they are important, so needs to make profit on the main games so it can help with the Paralympics and run Winter Olympics.

Honestly, I think it's all way too expensive. I also don't want Britain to host the games any time soon. The soft power thing makes sense, but only broadly.