I agree with the need for a midfield three, absolutely. However by accommodating Yaya as part of that three, you're forcing Silva (our best and most influential player when fit in my opinion) to play out of position as a wide forward.
The weakness against Liverpool was nothing more complex than a lack of work rate and fighting spirit. As I have said in another thread Liverpool won that game because we wanted to play but weren't prepared to battle for the right to play. Liverpool did the dirty work, they worked harder than we did off the ball, they were aggressive, they pressed high and made it difficult for us to play. We didn't and Yaya was the prime culprit, in terms of his lack of work rate and more importantly by his lack of leadership.
You say a much better player, in what respect? Other than Yaya's passing range, I genuinely don't know what else he contributes more than Sterling. You mention Yaya's 30 goals, yet Sterling has scored more this season even with the inclusion of penalties (of which Sterling has earned at least two to my knowledge).