You hardly ever see a dead anything, unless it's road kill. And the creatures that would consume road kill can't get to it very easily because of where it is; if it were still in the hedgerow or field it would be gone quickly.
Proof? I dumped a dead muntjac deer in a hedgerow on this farm. When I went by a day later, there was no sign of it. Same happened, though with more evidence, when I dumped one under a bush in the middle of a meadow. In 24 hours I could see some of the skeleton and flesh but by three days the only sign was a bit of the skull and the pelvis and a couple of verterbrae,all scattered over a wide area, where foxes had dropped them.
Birds are tiny in comparison, and weak, old , ones are likely to be killed and eaten quickly by predators even before the flies, crows etc set in.