Well, like a number of the new diagrams this one isn't actually there to get you from Rainham to Luton, it's really there to provide connectivity from the London area stations South of St Albans to LBG and to provide longer trains on the Dartford via Greenwich route. Rainham is just a way of mopping up the SE service East of Dartford operationally. This new link has been much debated over the past 18 months, as it obviously adds a new conflict on the LBG approach (the Thameslink project was designed to remove them at that location), and it has required slowing down the remaining SE services via Greenwich a little to fit it in. A potential routing via DMK and Blackheath has also been on the table for a little time but, amazingly, this route provokes slightly fewer conflicts, ie. Lewisham and Loughborough Jnc, (and is actually quite fast from Dartford - Deptford to the central core) so it's probably going to be staying for some time yet. Plus when people at these stations discover that it provides a quite good connection to Luton for flights all over Europe -- miles better than anything before the timetable change -- it will naturally develop its own fan following!
I think your not taking Crossrail into account, it'll parallel the line for a short bit between Abbey Wood & Woolwich but I can see it drawing passengers away from even the Bexleyheath and Sidcup lines it, they're rejigging bus routes in those areas as we speak to reach Abbey Wood and Woolwich Crossrail, Heathrow is Britains biggest airport an the Heathrow services will start at Abbey Wood as well as Reading Services, i seriously doubt people even in Greenwich will want to travel on Thameslink for over an hour to Luton when all they have to do is change at Farringdon and zoom to Heathrow, as for fewer conflicts we'll why did the Greenwich lose CX, because of the same conflicts being made now, the effect of this won't be immediately noticed but one delay could have a knock on effect on the whole network.
How is this better than what we had before? For us beyond Dartford it's a nightmare, before the 20th we had 2tph semi fast trains calling only at major interchange points, sure it wasn't the fastest but it's miles better than what we got now, crawling and calling at the minor stations, I can understand the need to call at stations on the Greenwich line since they would be downgraded to 4tph (though usage at Maze Hill and Westcombe Park have fallen) but they should have made this semi fast between Charlton and Gravesend at the very least
Whose to say in a few years when the Rainham becomes an unwanted millstone around the bosses necks they won't take this service away? The likelihood is probable especially once Crossrail is fully up and running they could justify withdrawing Thameslink from this neck of the woods citing Crossrail and the fact that it's likely going to extend to Gravesend in a few years time, I find it highly unlikely the rail bosses will allow this area to have both Crossrail AND Thameslink, especially once Windmill Junction is able to handle the extra services, if they needed to reach Gillingham then the best route would have been to do so via Denmark Hill & Catford, replacing the current Gillingham stoppers on the Bromley line.
