Where do birds and squirrels go to die?
A major cause of squirrel death is predation:


Survival and mortality of the Arizona gray squirrel (Sciurus arizonensis)
Causes of red squirrel (Sciurus vulgaris) mortality in England


You won't see those bodies, for obvious reasons.

Disease, starvation, and harsh weather are other major causes of death. Squirrels dying in these ways are probably likely to die in their nests or otherwise hidden places. Again, no visible bodies.

So that leaves being hit by cars as the major cause of mortality where you'd have a chance of seeing bodies. You've already noted that you do in fact see these bodies, so there's no contradiction there. I'll add that depending on where you live, roadkill can be cleaned up by scavengers more or less quickly -- in areas where buzzards, coyotes, crows, etc are common, they can be cleaned up quickly, but in more urban and/or colder areas they may last longer.