Last week, Fortune ran a very interesting story on how Southwest Airlines (LUV 0.61%) has been reinventing itself to appeal more to business travelers. Management sees long-haul travel and the business travel market as key areas where Southwest can grow as short-haul leisure travel demand declines.

Southwest Airlines is chasing more business travelers.

Southwest certainly has been retooling its business in the past few years, and the trend toward flying longer routes is very clear. However, the Fortune article overstates the extent to which Southwest is vying for business travelers.

In cities where Southwest is the leading airline, the carrier should be able to win over plenty of business travelers -- and in many cases, it already has. But across most of the country, Southwest isn't a big threat to American Airlines (AAL 1.47%), Delta Air Lines (DAL 0.21%), and United Continental (UAL -0.46%) in the business travel market.

Southwest has bulked up in big cities
Southwest Airlines has changed dramatically in the last 10 years. In 2005, it didn't fly to major cities like Atlanta, Denver, and Minneapolis -- and it only served huge metropolises including New York, Boston, Washington, D.C., and San Francisco through secondary (and typically inconvenient) airports. Today, Southwest flies to all of those cities' main airports.

By entering these key airports, Southwest has put itself in much better position to court business travelers as well as leisure travelers. But it has come at a price. These airports tend to be more expensive to operate at, raising costs, and are congested, leading to more delays (or forcing Southwest to build extra time into its schedule -- which also raises costs).

Sure enough, Southwest's non-fuel cost per available seat mile has risen from $0.0637 in 2005 to $0.0822 in 2014 (or $0.0852, including the impact of profit sharing).

Despite this big increase in costs, Southwest has been earning record profits recently. That's due in part to a less cutthroat competitive environment, but it also has a lot to do with Southwest's increased presence in the top U.S. business and population centers.

Legacy carriers have an edge with businesses
There's more to winning business travelers than having a presence in big cities, though. Most importantly, American Airlines, Delta, and United all have significantly broader route networks than Southwest Airlines. All three legacy carriers serve more than 300 destinations, compared to about 100 for Southwest. That makes them one-stop shops for corporate travel departments.

Legacy carriers have massive route networks compared to Southwest. Image source: American Airlines.

It's not a fluke that American, Delta, and United serve vastly more destinations. One key way that Southwest keeps its costs down is by operating a uniform fleet of Boeing 737s. However, these planes are too big to serve small cities and don't have enough range to fly more than about 3,000 miles. To offer comprehensive route networks, the legacy carriers need lots of different aircraft types, adding complexity and cost.

The legacy carriers also offer costly perks that are valued by frequent fliers, including first class and extra-legroom seats, airport lounges, and concierge-type services. Southwest keeps its costs down by sticking to the basics.

Finally, even in its biggest markets, Southwest doesn't offer as many flights as legacy carriers do at their hubs. For example, Chicago is Southwest's top city, with 247 daily departures. However, American Airlines and United Airlines both operate hubs in Chicago with roughly twice as many daily flights as Southwest.

Where Southwest can succeed
Thus, American Airlines, Delta Air Lines, and United Continental still have significant advantages over Southwest in competing for business travelers' loyalty. Most business travelers won't sacrifice their lounge access, first class upgrades, and numerous flight options for free checked bags. (Frequent travelers can usually get baggage fees waived, anyway.)

However, in cities where Southwest is the No. 1 airline, it should be able to snag a high share of the corporate travel market. Industry consolidation has led to a big drop in the number of airline hubs, so Southwest is now the top airline in many cities, including some pretty big ones like San Diego, Las Vegas, St. Louis, Nashville, Baltimore, Tampa, and Orlando.

Business travelers may like fancy perks, but what they really need is to get where they are going as quickly and conveniently as possible. If the choice is between a nonstop flight on Southwest and a connection on a legacy carrier -- even in first class! -- most business travelers would prefer the former.

Thus, if Southwest Airlines wants to attract more business travelers, its best play is to keep adding connections to top business markets from the cities where it is already the biggest airline in town. In their hub markets, the legacy carriers are the clear choice for most business travelers -- and will remain so for the foreseeable future.