I think Carragher is basically right here. The reason 3 at the back isn't played more is not so much that players don't fit the system, but more that it when the other team has 1 up front it's kryptonite, and pretty much everyone plays 1 up front these days.
The fact that there don't seem to be a lot of wide centre backs who can thrive in that role is more about the fact that when the other team has 9 or 10 men behind the ball behind 3 CB's, the CB's look ahead and it's 7 vs 9 or 7 vs 10 ( 7 vs 11 really with the opposing keeper able to come out and grab overhit long balls) and it's just too hard to squeeze passes in for most footballers, whatever position they play, apart from the very, very good passers.
It is possible to get better at it over time, and their comfort obviously varies, with someone like Blackett much more capable or it as a very young player than Smalling will likely ever be, for example.
If we have to squeeze Mata, Rooney and RVP in the lineup (and we don't), I'd rather see Pellegrini's 4-4-2 (which isn't a million miles away from some of what Van Gaal did at Alkmaar):
-------Rooney-------RVP----------
--Kagawa/Mata--------Januzaj/Mata
-------Herrera---NEWCM---------
Shaw---------------------Rafael/Valencia
--------Rojo-------Evans----------
--------------De Gea--------------
If Mata goes, Herrera would be a perfect fit at the top of a diamond like Italy used for much of Euro 2012, but we'd need 2-3 new midfielders, so that makes even less sense when you look at our squad.
3-5-2 will work really well against teams who don't press very high but want to dominate possession and against teams playing 2 right up front. Other than that, it's far more trouble than it's worth.
Another option, which won't happen, is just to sell RVP because he's older and Rooney-Mata is our central attacking partnership going forward, or at least loan him out this year as part exchange for the right player in return (Juventus for Vidal, Madrid for Khedira or Di Maria) with him getting CL football for the year and he can come back next year when we have an extra 10-12 games and there's enough for him and Rooney.
Finally, there's the option of using Rooney as a left-winger and hoping he figures it out, which I sort of think he would. He wouldn't have to do a ton of defending, and he's not bad at defending out wide anyways and if he doesn't want to finish 7th again he'll honour his responsibility as the captain and work his ass off there and figure out how to get double digit goals from the wing without top-end pace like Pires did.
--------------RVP-----------
Rooney---Mata/Kagawa----Januzaj
------Herrera---CM--------
Shaw-------------------Rafael
-------Rojo-----Evans------
------------De Gea----------
That lineup requires only one transfer (assuming Rojo is done) and it's good enough to pip Liverpool for 4th. Is the 3-5-2?