They overbook as the goal is to have a full plane and no shows will happen.
The only way to get full flights is to look at it statistically to assess probability of a no show and how many.
Some people on this thread apparently do not understand this business well enough to appreciate this.
Reminds me of planning for my daughter's wedding. They wanted x meals served at reception. We sent out invitations for more than x as we could plan for a range of no shows and we might be stuck paying for meals that would be uneaten.
Could this have resulted in some people that would not have meal if more showed up than planned? Yep, but it was unlikely based upon probabilities.
I said this earlier and it went over the head of a reader, but casinos operate with probabilities in a somewhat similar fashion, using Monte Carlo analysis.
I get what you are saying. There is a better way to deal with it. When the plane is full, put everyone else on standby. The no shows will create an opportunity to seat the standby fliers. If there are zero no-shows, then you didn't promise a seat, much less put someone in one.
The airline should know the seating arrangements on every plane, by tail number, how many of what are available, and the only time anyone would get bumped is if they have to change to a smaller plane. That would cut down on a lot of this.
The percentage of no-shows would also give the airline the flexibility to insert crew hitching a ride, or whomever they chose without bumping someone who had been told they had a seat.
It is in the optics. Put me on the plane, tell me I have a seat and I'm going where I'm going, as planned. Then tell me I'm not, and I'm not going to be happy about it. Tell me there might come an opening (before anyone boards) and let me fill it (those no-shows) and I'll be happy I got on. Presentation is key here. People are happy if they think you have done them a favor, and P.O.ed if they think you took something from them. So let them think they were done a favor rather than let them feel like they got screwed.
And sort out the passenger boarding before you put people on the plane, by class or whatever. Don't seat them and then want them to get off. That's just going to cause hard feelings.