The markets weren’t too surprised Monday when Singapore Airlines released a terse statement that it has entered talks to sell its 49% stake in Virgin Atlantic. The partnership that began in 1999 between the two airlines had become so unprofitable that Singapore was forced to write down the value of its stake in Virgin from S$1.6 billion to basically zero this year.

There is plenty of blame to go around as to why Singapore wasn’t able to make its venture with Virgin work. Singapore hoped the partnership would help it gain a foothold in the most profitable segment in the airline business – the transatlantic route between the U.S. and Europe. But both parties failed at executing any meaningful partnership agreements to allow that to happen; in fact, it was only last year that the two started codesharing their flights, something that should have happened a decade ago.

But after years of fruitlessly searching for a buyer, Singapore’s long, Richard Branson-fueled nightmare could be coming to an end. Enter Delta Air Lines (DAL). Virgin’s allure remains its lucrative Trans-Atlantic routes, specifically the New York to London route. Virgin has a number of extremely valuable landing “slots” at Heathrow Airport, which Delta covets. The conventional view here is that Virgin will transfer those slots to Delta, allowing it to expand its empire in the only other major European player.

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While some see this as a “no-brainer,” for Delta, any deal actually looks to be more trouble than it’s worth. First, if Delta wants greater access to Heathrow, it would be cheaper and easier to just buy some slots from another airline, preferably one that it doesn’t compete against. Why would Virgin turn over any of it slots to Delta, anyway? Contrary to most media reports, Virgin isn’t some Heathrow gold mine slot machine, it only controls around 3% to 5% of them and uses all of them, mostly on routes that Delta already serves, according to Deloitte. Just ask Singapore how many slots it got from its deal with Virgin: zero. Indeed, when Singapore recently needed a slot pair for a new flight out of Heathrow it was forced to buy them from South African Airways.

But what about connecting passengers? The thinking here is that Virgin Atlantic and Delta could codeshare flights to let Virgin passengers connect to points in the US out of JFK Airport on Delta, while Delta passengers could do the same on Virgin flights out of Heathrow. Have you ever connected through Heathrow to another destination? To save you the misery, the airport is always stuffed to capacity, making connecting a terrible experience for passengers. And if you think Sir Richard Branson is going to let Delta passengers from Chattanooga into his exclusive “clubhouse” lounge in Heathrow’s Terminal 3, you better think again. Not even first class passengers on Singapore Airlines can gain entry.

If Delta passengers need to connect to a destination not already served by its extensive network, they could do so more easily through one of its Skyteam partners’ hubs in Europe, which, compared to Heathrow, are a breeze to connect through. And when they land in Paris, Amsterdam, Madrid, Rome or Milan, Delta passengers can take thousands of flights serving hundreds of destinations. At Heathrow, Virgin can take Delta passengers to 18 destinations, most of which it already serves. Even if Virgin wanted to join Skyteam (it never joined Singapore’s Star Alliance), Virgin’s limited route network would be of little benefit to the alliance.

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If that weren’t enough, Virgin is also hemorrhaging cash. The airline posted a pretax loss of 80.2 million pounds ($129 million) for its fiscal year ending last February. In fact, the company’s losses for the last two fiscal years have wiped out all profits made in the last five. Virgin’s problem is that its business model at Heathrow is basically broken. The airline relied on the British airline BMI to feed up to 25% of its U.S. and international planes with domestic travelers. BMI had a massive 11% share of Heathrow’s landing slots – two to three times as many as Virgin. But British Airways blew up that cozy arrangement by recently acquiring bmi, giving the flag carrier 51% of Heathrow’s landing slots. While regulators have forced BA to relinquish some domestic slots to Virgin, they could never replicate BMI’s heft at Heathrow, leaving it scrambling for a domestic partner airline.

But Delta and its Skyteam partners are a poor substitute for BMI. While Skyteam’s European airlines could theoretically connect their passengers through Heathrow, it wouldn’t make sense as they could fly them directly to almost everywhere Virgin flies and beyond both faster and cheaper. Skyteam already operates the most flights over the Atlantic, with over 250 daily departures, so there is little need to add more flights, especially on the heavily traveled transatlantic route. Skyteam was granted anti-trust immunity by the US and the EU, allowing them to legally collude on prices. Regulators may not look too kindly on Skyteam adding yet another airline to the heap and could even go so far as to reject Virgin’s entrance into the price setting cabal. That would effectively kill any minute benefit that would come from a tie up with Delta and its partners.

But probably the biggest reason Delta shouldn’t get in bed with Virgin Atlantic is Sir Richard Branson, Virgin Atlantic’s billionaire founder and largest shareholder. His Virgin holding company owns the other 51% of Virgin Atlantic, giving Branson total control of the airline. Steve Ridgeway, Virgin Atlantic’s chief executive, told Bloomberg News that Sir Richard is unlikely to relinquish control of Virgin Atlantic as part of a possible sale of Singapore’s 49% minority stake. That should come to no surprise to anyone who has ever flown Virgin Atlantic or knows anything about Sir Richard at all. This is the man who recently commissioned four designers to create lifelike ice cubes of his head for passengers’ drinks in Virgin Atlantic’s tony “upper class” cabin.

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It is hard to see Virgin operate without Branson at the helm. The airline’s perks and amenities, from its complimentary chauffeured pickups for upper class passengers to generous baggage allowances for passengers in coach, fits with Branson’s whimsical disregard for convention which has made Virgin such a hit with its fiercely loyal customers. Without Branson at the helm, Virgin might as well just liquidate.

Branson has said that Virgin would probably need to join one of the big airline alliances in the wake of BA’s takeover of BMI, but that doesn’t mean he is about to give up control of the airline – let alone just give away landing slots to some Americans from Atlanta. Given all this, it would be best if Delta just invites Virgin to join Skyteam and saves its money for other things, like maintaining its new refinery or for buying some badly needed new jets.