People won't book a flight -- especially on short notice -- just because it's cheap. They book because they actually want to go somewhere. Sure, there are people who occasionally want to make a trip on a whim, and a higher price is a disincentive and deterrent to making that decision last-minute... but it doesn't automatically follow that low prices mean that they'll always be snatched up and there won't be available tickets for people who "need" one more.
Demand pricing (plus full fare flexible tickets and first/business class) is what helps less affluent people being able to afford a ticket at all. So instead of everyone having to pay a flat $600 for a seat, people with flexible travel dates can buy early and pay $300. They'll lose some amenities (like legroom, food, "free" baggage, etc), but for some people, that can make the difference between being able to afford a ticket at all or not.
If the plane is so full that the airline can triple the price over what they cost 2 weeks ago, it's likely that there would have been no seats at any price when I wanted one if they kept prices steady at $400.
I'm by no means wealthy and $1300 was painful, yet still I was thankful that I could get a seat at all for a very time sensitive trip.
When I had to fly cross-country due to a parent's sudden serious hospitalization, I paid an arm and a leg to book a fare for a same day departure, but I sure am glad I had that option, I'd rather pay $1300 when I really need to be somewhere than having no options at all because all of the seats sold out at $400.