I'm fully aware of the irony of this post coming on top of my general rubbishing of the idea, but...
One thing that Prince's Street would be useful for is protecting the Edinburgh to Glasgow link against problems at Haymarket. Any trouble at Haymarket causes major problems throughout the Central Belt. If Shotts, Carstairs and WCML services were removed from the mix, the pressure on Haymarket would be reduced, making failures less critical and easier to recover from. It would also be possible to operate an express Glasgow Central to Edinburgh Prince's Street service via Shotts, taking the pressure off of the Queen Street to Waverley route; the two lines used to be pretty competitive before BR picked Falkirk as the main line and downgraded Shotts.
Naturally, keeping it open would have caused more trouble than it was worth for all the reasons discussed above. But it's not like it would be totally without benefits.