The Abbeyhill turn back was necessary to allow 6tph of 6 coach E&G shuttle.
Eventually, this was descoped in favour of 4tph of 8 coach trains, with platform lengthening and Queen Street remodelling instead. This meant that the Abbeyhill turn back, Greenhill upper grade separation, a turnback at Croy from the QS direction, and the Almond Chord were deemed unnecessary.
Greenhill and Almond Chord are still on the agenda, and will come back into favour eventually. Furthermore, provision of new platforms (and one new crossover) at Waverley has allowed more, longer trains to terminate in bay platforms, both from the north and south. In turn this frees up through platforms, meaning you can stack up more trains at Waverley, and so running to Abbeyhill to turn back isn't necessary. The crossover has also meant more parallel moves are available, and you'll often see platform 7 used as a hot spare, and 8/9 (the suburban platforms) used to keep the Avanti out of the way.
The Abbeyhill loop was a proposal to regulate up trains leaving Waverley. It's been suggested as a solution to increased capacity between Waverley and Portobello Junction. There was never a proposal to reinstate Abbeyhill/Meadowbank stations. These stations would be too close to Waverley to serve a different area, would be served too infrequently to offer a useful service, and too close to very frequent bus links to really be worthwhile.
The Abbeyhill loop however runs into the problem of not gaining any time. If you dispatch a train from Waverley southbound in the ECML, the current headway is 2.5 minutes.
With the Abbeyhill loop, you send one around the loop, and one down the main line, however you still have to merge the loop train back onto the ECML, and indeed most likely cross it over the ECML towards Brunstane. It doesn't add any capacity, just theoretical capacity for disruptions and engineering works (Calton tunnel rebuilds).