Bought, unused time is the way that the phone companies make their profit, whether it be with dozens of unused minutes you have leftover at the end of the month, or the 59 seconds you bought but didn't use because you phone call lasted 61. It's an arbitrage opportunity. The point is that if they free up 59 seconds of airtime even though you've paid for it, they can do the same with the next guy, and they next. Ultimately, if you have 60 people make 61 second phone calls, that second minute of airtime made them 60x the amount of profit as if people had actually been using it.
The 15 second message is a way of pushing you closer to that magic 61 second mark, and I would imagine the length of that message (and thus the reason it still has that stupid "page this person" option) is calculated to set the average call length to leave a message right at the point where it's most profitable to them.