I'd say one of our biggest problems last season without Walcott, and a proper striker, was that defenses were not at all afraid to push up to minimize space between themselves and their midfield. They did that because they pretty much knew we were not in the least bit threatening them in behind. Podolski does absolutely nothing to change that, whereas Walcott with his pace and willingness to get in behind does exactly that.
A byproduct of this is that the center where Özil, Cazorla and Wilshere in particular like to operate gets congested, they are all less effective then, and we end up losing the ball way too often there. Lots of us complained last season that we had problems keeping sustained pressure on opponents; IMO a lot of that comes down to what I have outlined above. We simply couldn't push teams far enough down the pitch.
Saying that Podolski does anything at all to help with this is just bogus IMO, whereas Walcott is crucial for it. Podolski has decent pace, but 8 times out of 10 he wants the ball to feet, just like the rest of our lot. IMO Walcott is unique in our squad in that he mostly wants the ball into space, and he runs to make it happen. His involvement in our general play in this respect is either here nor there, because his runs keep defenses honest regardless. We desperately need another runner in our front line, and Podolski certainly isn't it.