Just confirming the above: The no-show rate is actually relatively stable in _most_ cases, which is why airlines try and optimize for this by selling past physical aircraft capacity.
In some markets it's illegal, in which case the average airfares are often notably higher.
This can have a more extreme effect than is immediately obvious: Because "last minute" fares (the ones that often fill up the aircraft) are usually the highest price and are critical in how airlines are able to make flights profitable.
Additionally, the most common no-shows are those who have booked early (the cheap tickets), meaning oversell allows the airlines to make space for urgent last minute travellers when the earlier ones don't turn up.
Without catering for no-show, it's feasible that air fares could end up a LOT more expensive (potentially 20%+) to remain profitable, depending on the distribution of prices in the demand curve leading up to departure.
You can certainly not do it, but on average, customers end up worse off (and the market is relatively good at optimizing this).
The biggest problem (in our mind) is that airlines don't have a good "safety valve" in cases where things go wrong. That's what we (attempt to) fix.
Oversell is sometimes known with high confidence at checkin-close (1 hour prior to departure) or even before, due to the fact that oversell thresholds can change throughout the booking curve.
Airlines don't have a current solution to rebalance/correct loads prior to the gate auction.
By overbooking, the airline can ensure that all seats are occupied, which means more people get to their destinations when they want to, and the cost-per-passenger is lower (as fares don't have to include the overhead cost of empty seats).
Most of the time their forecasts are accurate and the system works well for everyone. But occasionally their combination of forecasting, incentives to transfer and customer service practices go wrong, resulting in the horrible incidents we've heard so much about.