Whilst the works would be fairly expensive, they would also allow better connectivity for a LOT of people, for example the Aldershot Urban Area (station - Farnborough Main) is about 250,000 people.
That's on a par with Plymouth and Milton Keynes whilst it's smaller than the Reading Urban Area not by all that much (320,000).
On top of that by connecting to Woking you put Heathrow one stop away from Portsmouth, Salisbury , Andover and the like as well as improve the number of trains from Southampton, Winchester, Bornemouth which can be used to get to Heathrow with just one change (not only the frequency but the capacity of each train).
The suggestion of using the Hex paths makes sense if you are looking to also build the western approach, as those services would use the same paths as the Hex paths just on the western side. Something you can't do if they are being used for more services between Reading and Paddington (which may go beyond Reading).