We never hear from the other side of the equation. Those passengers who are able to book a seat that otherwise would be unavailable. But no one actually knows when they are in this situation, or appreciates that they have travelled despite all of the seats having been sold. The numbers of these are not insignificant ...
Some of the network airlines use very sophisticated programs (as mentioned above) and they almost always get it right. Impossible to always be right but very few of their passengers are actually denied boarding. Asking for volunteers (and rewarding them) does keep this number down, and you wonder why the airline mentioned didn't do so (it is the law!).
However I doubt that the LCC model would invest the significant sums necessary to enhance their already quite limited systems. It likely isn't even possible. And when they do bump passengers their ability to 'put them on the next flight' is a lot less than network airlines. They need to seriously consider putting their customers on other airlines in these situations - something they have failed to do so far. Yes there is a cost in this, but if done right, the cost is going to be a lot less than the revenues overselling generates.