That "problem" remains unsolved because it's actually a fundamental aspect of reality.
There is no natural separation between code and data. They are the same thing.What we call code, and what we call data, is just a question of convenience. For example, when editing or copying WMF files, it's convenient to think of them as data (mix of raster and vector graphics) - however, at least in the original implementation, what those files were was a list of API calls to Windows GDI module.
Or, more straightforwardly, a file with code for an interpreted language is data when you're writing it, but is code when you feed it to eval(). SQL injections and buffer overruns are a classic examples of what we thought was data being suddenly executed as code. And so on[0].
Most of the time, we roughly agree on the separation of what we treat as "data" and what we treat as "code"; we then end up building systems constrained in a way as to enforce the separation[1]. But it's always the case that this separation is artificial; it's an arbitrary set of constraints that make a system less general-purpose, and it only exists within domain of that system. Go one level of abstraction up, the distinction disappears.
There is no separation of code and data on the wire - everything is a stream of bytes. There isn't one in electronics either - everything is signals going down the wires.
Humans don't have this separation either. And systems designed to mimic human generality - such as LLMs - by their very nature also cannot have it. You can introduce such distinction (or "separate channels", which is the same thing), but that is a constraint that reduces generality.
Even worse, what people really want with LLMs isn't "separation of code vs. data" - what they want is for LLM to be able to divine which part of the input the user would have wanted - retroactively - to be treated as trusted. It's unsolvable in general, and in terms of humans, a solution would require superhuman intelligence.
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[0] - One of these days I'll compile a list of go-to examples, so I don't have to think of them each time I write a comment like this. One example I still need to pick will be one that shows how "data" gradually becomes "code" with no obvious switch-over point. I'm sure everyone here can think of some.
[1] - The field of "langsec" can be described as a systematized approach of designing in a code/data separation, in a way that prevents accidental or malicious misinterpretation of one as the other.