And without over-booking, your tickets would all cost more.
That depends on the business model. I would argue that point today since now days most LCC operators manage quite well without adopting an overbooking policy. If a seat has been sold on a non refundable basis then there is no need to overbook. Empty seats can eventually be used to accommodate (paying) stand-by or staff pax etc. Overbooking was rampant back in the days when it was easy to make a telephone reservation (or even multiple reservations on the same sector on a given day) without any financial commitment until turning up for the flight eventually chosen. This was particularly rife in the USA where it was not uncommon to see no-shows exceed a staggering 20-30 % on some routes. That was a time when overbooking was a necessary tool of the trade.