Why would someone book a flight using a service other than Google Flights?
The simple answer is that you can not book a flight via Google Flights. Google is not an airline or a travel agent. They are a search engine. They provide meta data searches for travel. aka meta engine. Just like other meta engines - Expedia, Momondo, and Kayak. Meta engines give you links to sites that can book and buy tickets.
You would NOT use Google Flights (or a meta engine) if you wanted to get a complete list of flights available or the lowest cost flights. Google Flights and meta engines forward there prime advertiser products that fit your social profile. This may eliminate flights and lower cost options. In some cases you are only given the 1 purchase path.. the best path for Google Flights to make a profit.
Do your shopping. Come see us at Future.Travel to see how realtime inventory works. Google Flights is giving you cached data from history. A good OTA gives you real time time display of seat/price inventory.