Overbooking
 

While it is true that this has been an industry-wide practice for years, didn't it get started in a time when passengers could cancel their reservation and get their money back? This led to passengers booking on several flights, taking one and leaving the airline with open seats on the others.

That is no longer true. Today passengers are charged for unused tickets. Since the basis for allowing airlines to overbook has ended (or, at least diminished) shouldn't allowing the airlines to overbook also end?

Alternatively, why not offer tickets that guarantee the purchaser a seat?

But it still helps to keep prices down (or profits up, perhaps).

If anything, I think that the new non-refundable and non-changeable Basic Economy fares all the legacy airlines are introducing will actually require even more overbooking, because passengers flying on these ultra-cheap fares will have absolutely no incentive to notify the airline of a change in their plans (since they will gain nothing by doing so).

You're mixing up "could cancel their reservation and get their money back" and "does cancel the reservation and refund", or change it after you no-showed, same thing.

They are not the same. If every single ticket sold is refundable and changeable at any time for no fee, if no one ever no-shows, the overbooking rate would have to be zero. But if every single ticket sold is totally nonrefundable (100% Basic Economy), and 10% of passengers no-show, then you could overbook by 10%. Why someone would no-show is a myriad of reasons, one of which is whether the ticket is restricted/use-it-or-lose-it, but many other reasons as well which is why people still no-show on Basic Economy type tickets, not just refundable tickets.

Plenty of airlines offer fares that can be refunded or if cancelled receive a full or partial credit (after change / cancellation fees). Yes, there are LCC that do not, but they don't make up the entire market share.