If your building site never has earthquakes, that can work well. Otherwise an earthquake might put some part of the structure under tension and cause it to fail.
(Think of how hard you'd have to shake the Great Pyramid of Giza to make it collapse. That's not concrete obviously, but it too is under compression almost entirely, except for the corbel and lintel ceilings. The proper arches used in Roman concrete construction show that with the right engineering you can push unreinforced concrete pretty damn far. The Pantheon is probably the most impressive example of it. Compare how well it's withstood earthquakes with the Colosseum.)