In http://www.straightdope.com/classics/a991126.html, Cecil writes this line:
Why not put the counter on the tens column and ignore the ones column? Because that would get you a snooze which varies from a few seconds to ten minutes.
Let’s have a hypothetical clock which monitors the tens column for snooze. Imagine hitting snooze right as the clock turns to 7:30 - in ten minutes, the tens column will change from a 3 to a 4 and the alarm will go off again. But what if we hit snooze at 7:39? Then the alarm will still go off when the tens column changes to a 4 - in under one minute.
The only way to get a snooze longer than nine minutes would be to monitor both ones and tens columns. That would require additional parts, thereby raising the cost and complexity of the clock.