I don't understand why it's not possible. You're asking if it's possible in the language. I don't see anything stopping you from, as you say, writing your own framework, or simply doing it in TF. Perhaps my ignorance of Julia is showing :)
But there really is a profound difference. The thing is that Python is really just a language to rearrange networks of nodes written in C++. A node written for one ML framework will be incompatible with a node written in another language. If you want them to work together you need to spend a lot of effort gluing them together, and most likely the performance benefits are lost.
This is very different in Julia because you are using pure Julia code. What is specialized C++ nodes in Python, are for the most part just plain functions in Julia. There is nothing special about them. That is why they can be used anywhere.
In Python frameworks each of these C++ nodes need to contain information about how auto-differentiation is done. That is why they are tailor made for one specific ML library.
In Julia the whole automatic differentiation stuff is perform code transformations on regular Julia code.
Are you familiar with LISP, and the idea of code as data? That is what we are talking about here. A regular syntax graph of regular Julia code gets manipulated to do autodiff. You are not organizing C++ nodes in a network.
That does sound very different than Python. Admittedly, I haven't used Julia, because I never had to for professional purposes. For personal projects, I use PyTorch, because I find it easy to use, intuitive, and I have a lot of experience with it. Maybe one day I will be forced to use Julia and will appreciate what it brings :)
I don’t much use Julia, but it is a beautiful language. I started a tiny side project for using Julia for non-numerical things like querying SPARQL endpoints, text processing, etc. Julia could be a universal, use for almost everything language.
It's not that it's not possible. Yeah, you could always "write your own framework".
It's that it's not readily available by the language, ready-made to compose, without resorting to external libs on C/C++/Fortran, and so on.
So, "not possible" not in the sense that "it's not possible to write a program that solves the halting problem". More like "it's not possible to write a web app in assembly". Which means, yeah, it's possible, technically, but you wouldn't like it, it would be full of holes, a pain to maintain, and not a good time investment.