My wife and I flew UAL Corp.'s (Nasdaq: UAUA) United to New York on Friday. We were in town for my cousin's wedding. Why should you care? Because United bailed out on a chance to pad its profits by at least $90 during our flight, and perhaps much more.

Here's how. United divides cabin seating into first class, "Economy Plus," and basic coach. Economy Plus includes the first few rows of coach, extending to the exit rows. Seats in this area have a bit more legroom than those in the back of the plane.

And they cost more. Frequently, when I log into United's website to buy seats, I'm asked if I'd like to upgrade to Economy Plus for $40 to $50 per seat. "No" is my boilerplate answer, as I suspect is the case with most fliers.

But something interesting happened on Friday. Our plane was mostly empty. Economy Plus, in particular. When the doors closed, flight attendants announced that they would not tolerate passengers from the back moving into open seats in Economy Plus. We hadn't paid for the privilege.

I agree that those seats are United's to sell as it sees fit. And yet it's not at all kind to rebuff those passengers -- several, on our flight -- who would pay to get out of a sardine-sized middle seat when an open chair is available in the front cabin.

But that's how it is. Want to upgrade to "EP," as some call it? Answer "yes" when booking the next flight.

Could United really be this dumb? It appears so. Our rather accommodating flight attendants told me that upgrades couldn't be processed in-cabin because, once on the plane, everything is a cash business, including food.

Not true. You can't use cash to make an in-flight phone call. Only a valid credit card will allow you to do that. Why not take this same technology and use it for processing hot food orders, as JetBlue (Nasdaq: JBLU) does? Or, better still, for squeezing cash from empty premium seats?

United has an opportunity here. American Airlines parent AMR (NYSE: AMR), in trouble for maintenance woes, failed at monetizing a roomier coach cabin. Other legacy carriers, such as the equally troubled Delta (NYSE: DAL), have yet to try. Still others, such as Southwest (NYSE: LUV), figure that all you want is to get there, no matter how uncomfortable the trip may be.

My guess is that all three approaches are wrong. We're a nation of impulse buyers and yet there's no mechanism to "impulse buy" your way to better seating on any domestic airline. United is in the best position to change that. Let's hope, for shareholders' sake, that management has the courage to try.

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Fool contributor Tim Beyers owned shares of Southwest at the time of publication. You can find Tim's portfolio here and his latest blog entry here. Tim also contributes to Rule Breakers. The Motley Fool's disclosure policy has cleared your portfolio for takeoff.