What is overbooking (of flights), and why do airlines all seem to do it?

If rebooking is allowed, then "sell every ticket" does not equate to "fill every seat", since the passenger who moves to a different flight for a small fee takes up a seat in that other flight. Rebooking is a privilege that has been around for a very long time; taking that away from passengers is going to annoy business travelers very much, so it's unlikely to happen.

To compensate for the loss of revenue from empty seats they might have otherwise filled, airlines would most likely have to increase their prices, and thus become less competitive. It appears that there are too many people who don't care quite as much about personal comfort as long as the price is low to make "half-empty economy class" a viable business model. In the end of the day, airlines want to maximize profit, and if they can increase profits while alienating only a small fraction of travelers (including you, unfortunately), they'll go for it.

For an experience that is similar to a half-empty economy class (but with better food), I recommend flying business class - you pay a premium, but get more space and better service.

Note that maintenance rules for airplanes are set up regarding the number of hours flown, which means that the maintenance costs of an airplane are about the same whether it flies full or empty.

Let's say there are 10 seats, all sold at 100 dollars. However, this flight actually costs 1050 dollars to operate. So, in order to cover their costs, they could either charge 105 dollars per seat, or do the same 100 dollars per seat, and overbook (and get another $50) , because their computers say there is a very good chance someone will miss the flight.

The airlines have years and years of data on how many people will show up and who will miss the flight for every single combination of variables - Wednesday night in El Paso in March? Sunday night in Las Vegas in August? They know who exactly who did and didn't show. And, on the other side, paying people out that they overbook, they all try to avoid the involuntary bumping requirements (which are actually a good deal for the customer) and try to make it a voluntary bump and pay you off in airline credits instead.

Running an airline is not a very profitable business, and the actual "revenue per flight" is really much lower than people think it is.

Short answer - vote with your dollars, but time has proven people only care about the price, and everything else people "say", when the chips are on the table, the lowest cost will just about always get the traveler's vote.

The main issue is that, even if your own ticket does not allow it, most airlines do offer tickets that can be canceled or rebooked at little or no surcharge and they want to be able to continue to do that. They could in principle stop offering that service and avoid any need to overbook. They could also still allow changes or cancellations and just make sure they never fully book an aircraft to reduce the risk of having to bump or reschedule some passengers.

The problem is that someone has to pay for it (the passengers who want to cancel a ticket and can't, the airline if it has to risk flying with a few empty seats, etc.) Alternatively the airline could push these costs to the customer but it would make the tickets more expensive, possibly put them at a competitive disadvantage or annoy the wrong customers.

Note that people flying low-cost or buying the cheapest non-refundable non-changeable economy class tickets are probably the most price-sensitive. Next time around, they are still going to go to the cheapest airline so there is nothing to gain by offering them a better service at a slightly higher price. I have had a few bad experiences with EasyJet but I still fly with them from time to time because they are usually much cheaper than the next airline on some destinations I want to go to (no overbooking in this case but other problems). It is profitable to overbook passengers like me on a flight to offer them a cheap ticket and fill the plane but bump them to offer some flexibility to customers paying more.

The airline's goal is to have someone pay something to offset the huge fixed costs, hence overbooking, yield management, etc. The question is who is ready to pay how much and for what and how to correctly discriminate between these different classes of customers. Airlines might be getting it wrong but they definitely looked into it and chances are that increasing the cheapest tickets' price or stopping to offer flexibility for higher class fare would mean losing some passengers.

Would it make sense for passengers to push airlines to adopt other solutions (such as charging 10%-20% more for tickets, to compensate for the lost "overbooking" option)

NO!!! Very few people are ever inconvenienced by overbooking, but everybody would be massively inconvenienced every time they flew, if the tickets were 10–20% more expensive.

Alternatively, if you proved me wrong by demonstrating that people were prepared to pay 10–20% more for flights, I can tell you exactly what would happen. The airlines would say, "Thanks. We're raising ticket prices by 10–20% and, guess what? We're still overbooking you. So long, suckers!" As a real-life example, British Airways was making a loss on Concorde until market research revealed that most people thought tickets cost about twice what they actually did. BA took this as a big ol' hint that people were prepared to pay more to fly on Concorde and, bingo, it made a profit from then on.