I have always been a little intrigued by this proposal. East Grinstead does not need a better service than it currently has (outside the peaks), yet I have the impression that there is a proposal to run trains from Peterborough!
The same basic point applies to the Brighton - Bedford service that has run for years. The rationale is basically that they are running 4 tph to London from both Brighton and Bedford, and by connecting them together the whole thing operates more efficently. In the last year or two we have had the reinstatrement of through services from certain 'SE origins', but the vast majority of passengers from those areas probably aren't at all concerned where the trains go to north of London, because they all get out at Blackfriars or City.
Ultimately it will be the same for East Grinstead - probably a majority of peak passengers will not travel further than the core stations.
The advantage for the rail system as a whole is that 24 extra tph from north and south can't be easily terminated in the existing stations - that sort of frequency needs 6 -8 terminating platforms to run reliably - so by linking across London and sending relatively empty trains to the other end of the route everything runs reliably. For the Thameslink 'inner pairs' of stations of course a down train can return full again in the same peak period - this isn't necessarily the case if they pair off say Brighton and Peterborough of course.
It would be intersting to know roughly what fraction of current Thameslink passengers ever travel through from end to end - I suspect other than airport traffic there aren't many doing the whole route. That leads me to believe that at individual passenger level it doesn't matter where the new services go once through London...
PS - I don't think the peak services, say 4 tph, will actually run all day. All the RUS proposals I've seen are pretty clear that they are describing the morning peak service patterns - as it is always the most complex, and everything else is easier to manage...