Lots of good stuff here -
http://www.subbrit.org.uk/sb-sites/sites/s/scotland_street_tunnel/index.shtml
And a bit here -
http://en.wikipedia.org/wiki/Edinburgh,_Leith_and_Newhaven_Railway
There have been lots of 'ideas' for using it - because it's there more than because it's 'the answer to a real problem'.
It's quite steep (though not as steep as Dublin Street - which has had 'plans' for a bike lift).
Main problem is that it reaches Waverley at track level.
It *could* have been incorporated into Waverley Market (Princes Mall), it *could* have been a weather avoiding link to the bus station.
But-this-is-Edinburgh.
It's not London where the tube infrastructure is generally easier to create due to clay rather than igneous geology.
I assume LRC's Metro plans involved routing under the Waverley running lines, Cowgate etc.
One reason it didn't happen (apart from the money) is that (some) Newington residents didn't like the idea of it popping up near their houses.