Is this a structural weakness of Feistel networks?
If such a network had only a single round, then you might have a valid concern. This is why there needs to be least three rounds, so that every bit from L can potentially affect every other bit from L (via R from the second round).

It isn't a structural flaw, because multiple rounds are assumed. Changing this round structure would mean that it was no longer a Feistel network, and you would lose the reversibility of each round (when the key is known).