There are plenty of reasons to have a PPV in between the Rumble & Mania . . .
I. For starters, it makes WrestleMania feel all that grander (when done right anyway and even then, YMMV I suppose). Instead of just having one PPV focused on the build to Mania, they now have two. The best simile I can come up with is that it's like having two movies to build to swan's song in a series rather than just one. I guess I could just call it the trilogy effect. Granted, if WWE really doesn't book it in such a way, it kind of loses purpose, but that alone doesn't make it a bad idea. Moving on to bigger reasons . . .
II. It allows for an easy excuse to have the Elimination Chamber bout. This year's N1C's match for the World Heavyweight Championship is a perfect example, it's done for the last ditch efforts to secure a main event slot at WrestleMania (tying it into the previous one) after failing to do so at the Rumble prior. So, pretty much, instead of having to create one big angle or some multiple angles that will all cross paths for an Elimination Chamber match, they can use it for something akin to the Rumble's purpose here. Granted, this isn't entirely pertinent to each of the previous events but it's still a valid reason, even if the reason is essentially laziness.
While they could do a tournament that takes place over the course of a couple of weeks of Raw/Smackdown, it definitely is going to garner them as much money as having a PPV with the Elimination Chamber featured on it. Being a business, they're going to go that route. I could just have money listed as a separate reason here, but that's one that's obvious to everyone so, I'm just throwing it in here now because it's a big part of this one in particular.
III. It allows for feuds to continue and/or close in a smoother manner and still on a grander stage than a regular show like Raw. Take Shawn Michael's feud with JBL back in 09, one of my personal favorites (despite not seeing the resolution). That feud wasn't done by the time the Rumble was finished, and for all the time they spent focusing on the program, it would've been a damn shame, as well as incredibly anti-climatic, for them to wrap that up on just another episode of Raw so Shawn can start feuding with Taker. Angles of that caliber still need to be resolved on a PPV, for a business and narrative reason, ridding the PPV in-between Rumble and WrestleMania would cease that option.
As another example, without Elimination Chamber this year, what do you propose they do with The Rock situation? The only real options are have Rock focus solely on his re-match with Cena for the two months they now have or give Punk his re-match on a regular Raw, and neither really seem like the smartest idea to me. Keep in mind, that WWE have Punk/Taker set in place barring Taker deciding against competing for health reasons, so you'd have to incorporate. The only thing I can think of is having Punk dick around during the Cena/Rock stuff for awhile, trying to say that should be his match with Cena, he's still champ, rematch clause, yada yada and if Taker decides to not compete then you can just add him to the match. If he doesn't then left with the awkward transition of Punk's role, ultimately feeling like the last few weeks he was just filler, waiting for Taker to arrive at a decision. And yeah he was, but it shouldn't come off like that.
I would continue with other reasons but I'm going to stop partially because that last paragraph actually touched on the others, even if lightly.