Would be great to see but cost of this would surely mean the chance of this being delivered in the next 30 years is very slim.
Getting a version of the Airtrack scheme back on table seems to be much more feasible and deliverable. This could deliver a pretty easy single change journey at Clapham Junction or even maybe East Croydon between LGW and LHR, particularly if a stop was added to the Gatwick Express and the timetables co-ordinated.