I understand one benefit of the TL Programme was to relieve London terminals to allow other services to run a higher capacity service into there whilst ThamesLink trains went through the core and terminated elsewhere but I think Bedford for a service from East Grinstead especially is a bit too far out and might not be the best use of resources.
East Grinstead is less far both in mileage and (just) in time than Brighton, though.
it seems the general consensus is split on who wants Thameslink and who doesn't?
Other than perhaps a very small minority of people who would complain at any change even if everything worked perfectly and they weren't inconvenienced in any way, I don't think anyone really doesn't want there to be a good cross-London service. The problem is the shambles it's turned out to be.
The East Grinstead route is a prime example of why it's really unclear who some of the new routes are intended to benefit. It's a limited rush hour only service (replacing the previous limited rush hour only service to London Bridge), so no use for leisure journeys across London. At the times it runs the only use of it is to get to central London and back. The only benefit it brings is for the timetable itself.
And that's the big problem - the new timetable is trumpeted as if it would improve things for everyone with no exceptions, which just isn't true. The timetable is a reaction to "where on earth do we send the 24tph we promised", not to genuine passengers flows (existing or desirable new ones), it's for the railway's convenience (or as it's turned out, inconvenience), not the passenger's.