The Reagans and Bushes had homes to go to for vacations. The Clintons would have had to go to the governor’s mansion in Arkansas. The Obamas would have gone to Chicago to stay with the Rezkos or the Ayers, or a hut in Kenya.
They had a large house in Chicago.
This was no shack. However, looking at it you can see the security problems it would cause. So, they could have bought a set-back gated estate, or they could have used Camp David. (snort -- I know, right? Camp David was good enough for the hero, Dwight Eisenhower, who save Western Civilization, but not good enough for the community organizer.)