COCL2, As kbrockman says, its extra complexity. If you look at how closely spaced the spars are, you will get the idea. Each individual tank would need plumbing and fuel probes (gauges) too.
I don't know the typical wing depth on the F-35, but as an example, some of the Eurofighter Typhoon fuel probes are not much more than 4" tall (suggesting the tank is a similar depth), so with that sort of wing depth, the thickness of a bladder could easily reduce the tank volume available by 5% or more.
