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Purely functional programming languages solve the problem of memory allocation
No, they don't. You can write a program that will run out of memory or cause a stack overflow in a functional language. The problem of memory allocation isn't just "when should I delete some pointer."
Forget languages: You have a computer with finite resources and you have some algorithm that you want that computer to perform. "Solving" the problem of memory allocation would mean that your compiler (in whatever language) would look at your program and tell you up front either "Yes, I can run this program and it will require N bytes of memory" or "No, there is not enough memory to run this program."