They like to keep seats available for last-minute business travelers.

On routes where they have solid historical data that there won't be many of those, they actually do offer cheap seats and in some cases cash+miles awards. (Varies by airline.) Granted, the cheap weekend deals that used to rock in the late 1990's haven't been very good in recent years, but they still technically do them. I suspect that capacity cutbacks have tightened up even the off-peak flights. I flew this past Sunday and even the 8AM flights were oversold. Those used to be great candidates for the getaway fares.

Now the economy is growing but the airlines are keeping a lid on total seats available, making the odds of finding empty flights far less than it was in the past. I get the sense that no airline wants to be the first one to pour a ton of new seats into the market.