It’s not a bad idea, although, as other people have mentioned, it makes more sense to have 3 or 4 host countries. The issue, of course, becomes 1) picking the countries, and 2) getting those places to commit.
Yeah, L.A., or Tokyo, might think this is a good idea. They get press and an influx of tourism every 4 years. But, are they going to commit to it for the next 30–50 years? I don’t know, that’s a hard sell.
Basically, what seems to happen is that developing countries like to use it to announce their “world-class.” That’s why Beijing worked, and why it was worth it to them. Places that don’t need the prestige, don’t find it worthwhile.
Of course, that cuts both ways. On the positive, you have a bunch of cities and countries for whom there is actually a benefit. On the other, you risk a Rio, where a country/city that isn’t established as being stable is in charge of the Games. This would, obviously, be an even bigger deal for a city committing to doing it regularly.