Of course I could be dead wrong, but I'm just looking it from more logical, contractual, and logistical standpoint. It would be easier to do an expanded universe when you have time to work with younger characters, younger actors (which are more willing to sign longer contract obligations) and more freedom with continuity - not to mention sticking with a First Class timeline would be starting from scratch really.
And as if Hugh Jackman, Halle Berry, Anna Paquin, Ellen Page, Daniel Cudmore, Shawn Ashmore and the new additions to DOFP won't sign up for two more films. Who knows if some of them already signed for 3 films when they signed up for this film.
This reminds me of back in 2006, when people kept saying it was gonna be impossible for FOX to bring back the original cast for a 4th X-Men film. FOX didn't have a problem at all bringing back half of X3's cast in this movie and I'm sure if Cyclops/Jean Grey/Nightcrawler/OldBeast/OldMystique are in the script, the actors that portrayed them in the original trilogy would have said yes right away.
And that the thing you are really forgetting about is how would these films perform at the box-office. Its one thing for these films to be good but if they don't perform great at the box-office and they don't live up to the expectation of the studio. This series would be in trouble. Could you really picture a Second Class film/Third Class film outgrossing X3? People would just view them as prequels since they are set in the past and prequels usually don't outgross the original series. The only prequel series that really got a lot of money was the Star Wars prequel trilogy but if you adjust the ticket prices, Phantom Menace didn't outgross Episode IV, Revenge of the Sith/Attack of the Clones didn't outgross Episode V and VI and there's a huge gap between SW's original trilogy and SW's prequel trilogy unlike with X-Men's original trilogy and First Class.
I just don't see X-Men being in-demand again like it was in 2003/2006 and right now, if they move forward with the cast of First Class. The general audience were definitely not that interested with Origins/First Class and now with The Wolverine before they hit the theaters, simply because they are spin-offs and featuring a brand new cast. Even if X3/Origins were good movies, I don't think people would have been very excited to watch Origins/First Class especially compare to the hype that X3 received back in 2006. Another movie with the cast of First Class after DOFP could probably outgross X1/Origins because of 3D/increasing ticket prices, but they wouldn't outgross the upcoming/recent films from DC/Marvel. At least if they move forward with X5/X6 with the original cast, even if they don't outgross X3 or DOFP, at least people wouldn't say, it didn't do well because it was a prequel or it didn't feature the original cast or it didn't feature Wolverine.
I feel like this series is now in much better shape compare to 2009 to 2011. Its like the good old days where people are really looking forward to a new X-Men movie and there's a lot of excitement. The original cast that made the X-Men films a hit and they had a couple of records at the box-office are back, Bryan Singer is the director again, we have the characters that are really well-known to the X-Men universe and to the general audience. They shouldn't screw this up by releasing another prequel and giving the original cast another break. Prequels may be obsessively consumed in the comic book world, but they often amount to fanboy fantasias as far as the mainstream is concerned. If these back stories were so essential, then that's where the franchises should have started. The story needs to progress, not regress.