Does it need to? There is no particular need for fares via Staines to be cheaper when travelling beyond the Central London Terminals. It will know if a passenger interchanges at Paddington or Waterloo off a GWR or SWR train. Clearly there are other routes which avoid intermediate gatelines, including the Elizabeth Line.And if you tap out at Finchley Road, how does the system know which way you travelled?
I don't think it would be unreasonable to have a separate gateline for platforms 4 to 6 at Reading in any case if it really is a problem. It is a somewhat isolated part of the station since the rebuild.