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.
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.