Well, mainly because you could be anywhere within the application when this occurs. The countdown is sort of a "background process" running, allowing you to continue to work. Popping up a dialog when it ends is annoying and intrusive.
I'm not saying that's the wrong thing to do. Maybe it's the right thing to do. Now that I'm thinking about it, you can currently start a countdown then remove all of your players while the countdown is running, effectively putting you into the situation that not allowing the countdown to start is trying to prevent. So what happens today? I suspect before I go and look that the countdown simply ends. (Ha, I just tried this and the tournament starts and then immediately ends, because there are no players left. That would be a bug.)
2.6 has a setting for what to do at the end of the countdown (start the tournament, start the tournament with the clock paused, do nothing - just end the countdown). Maybe I should just add some text indicating that the countdown will just end if the tournament isn't "ready".