Is there a fundamental reason that plants cannot fix their own nitrogen?
That is an interesting question. But rises some line of thought by analogy, e.g. why people won't evolve to produce their own ATP without mitochondria? (I mean of course Eukaryotas in general). I don't see any reason why multicellular organism cannot incorporate bacterial functionality either as happened with mitochondria, or as just separate cell type, that will provide desirable enzymatic reactions.

The answer, no matter how unsatisfactory, might be simple: because it so happened. We definitely can create experimental conditions lacking N-fixing bacteria as well as varying amounts of nitrates, nitrites etc. And then produce and screen line of mutants for ability to fix nitrogen without symbiotic partners.