This is a fairly common and EXTREMELY useful feature that's been requested in the past. Not only does it allow you to "shift" large portions of the map, but lets you make complex patterns to be placed elsewhere and generally speeds up the entire tile-laying process as you don't have to move the cursor all the way to the tileset just to change tiles - you can pick up nearby ones. Suggesting you export your tilemap to an entirely different program, make one change, then import it back into C2, is pretty silly!
Also instead of select,copy,paste,etc. it'd be quicker to have a tool where you click+drag to "pick up" the tiles and when you un-click it switches to the draw tool.