Some managers would actually go for this and make it work. Mourinho is one I could imagine playing this kind of set-up, as he did something similar with Inter – Milito up front, Eto'o and Pandev on the wings with Sneijder pulling the strings in midfield. Very similar to what you suggested.
However, I don't think Rodgers should go this route, because the way to make it work is completely opposite to the way Rodgers' teams have been playing at their best – high pressing, dominating possession, relatively high defensive line. If you want to retain possession and play pass-and-move football, placing Sturridge, Benteke and Ings all up front is a pretty terrible idea because they will take chances and lose the ball and there will not be enough pressure to get it back immediately (as Sturridge and Benteke both don't press), so we'll be vulnerable to counterattacks. We'll be setting ourselves up for failure. Notice that in those games when Rodgers found himself in a desperate situation and subbed in a 3rd striker, this has to my recollection never, ever resulted in us getting the goal we were craving – but we sure conceded a few in those situations.
Like I was saying before, for now (when he comes back from the injury) Benteke should be dropped in favor of Ings and Sturridge and Ings should both play up front (no more 4-3-3 business). Some posters said it was the height of stupidity to bench your £32M striker, but the fact is, we scored 3 goals in a game for the first time this season without Benteke. And that's not a fluke – we also created a lot more quality scoring chances in the 3 games he wasn't playing. I don't hate Benteke, but I think the team style and cohesion is much more important than any player, no matter how much they cost.
