For less than 120 years the Olympics have changed city. For several hundred years the Ancient Olympics were held in Olympia, Greece. The benefits to each host city are not clear-cut, as it often takes decades to recoup the cost of the Games. As an alternative to hosting the Games in a different country each time, a country could bid to be the host of the Games in the 'designated location'.
No, the Olympic Games should not be permanently hosted by the same city as it is a global event, and as such, it should be represented globally. No one nation has a monopoly on the Olympic Games, and it should stay this way. To do otherwise would be to rob the Games of their global nature.
The entire idea of the Olympic games is that various countries compete. It should be hosted in various places to reflect the diversity and different cultures that are competing. It would show respect for the various nations, for the diversity of the Olympics, and would be more fair if it were held it different cities.