In particular, the syntax tree is also Just Another Representation of the functionality... But it's still way overspecified, compared to your intent, since it has lots of implementation details encoded in it. Actually it is the tests that get closer to an exact representation of what you intend (but still, not very close). (This is also why I love React and declarative programming: because it lets me code in a way which is closer to the model of what I intend that I hold in my head. Although still not that close).
So, programming seems similar to the mesh data for a model to me. The more you can get a representation which is faithful to the programming intent, the more powerful you are. LLMs demonstrate that natural language sorta does this.. But not really, or at least, not when the 'compiler' is a stochastic parrot. On the flip side it gets you part of the way and then you can iterate from there by other methods.
