I don't understand people who are conflating the search for HQ2 with Olympic bids and sports stadium bids. The Olympics are most likely a one time thing for a month, although in the future I could forsee it revolving around qualified sites, it takes a lot to convert facilities used for the Olympics into regular infrastucture (see Atlanta and LA).
Stadiums I think overall have a better impact, as they can create or revitalize an economic area, provide longer terms jobs, and sports teams provide back to their communities.
Amazon is on a completely different level. They will bring thousands of skilled workers, and generate trillions in economic activity. HQ2 will stand for a long time, it can completely change the trajectory of a city. There are many many issues with bringing Amazon to your city, home prices and infrastructure to name a few -- but isn't this a problem you'd rather have than not?