Is this problem even solvable on a fundamental level?

Of course, they can work on preventing nodes forwarding hidden header information, but an entity with global network insight will always be able to correlate users by the timing of their transmissions alone.

The introduction of malicious nodes is a workable option for lesser players. But hidden in the realtime nature of the Tor network is always the possibility of deanonymizing users if you're a powerful agency that can afford to inspect a sufficiently large part of all network traffic - they don't even have to run any nodes themselves.