Don't worry, we are exactly the same here, There are literally dozens of fallen birch among the 980 hectares of Chopwell Wood.
It's a bit strange really, you get perfectly healthy specimens with a few dead ones lying around among them. It's always been the same, wherever I have seen birch growing in decent numbers, there are always dead ones.
This has several benefits to the camper/canoeist/bushcrafter of course, as you always get polypore fungus on both standing and fallen, dead birch as well as plenty of easily available bark for fires etc.
The benefits to wildlife are huge; woodpeckers can easily dig out insects as well as nest holes in rotten birch and owls and bats often take over these woodpecker holes later on.
regards
R.B.