It seems noble to solve a problem outside of your sphere of responsibility. If you’re solving this problem because there is no permanent responsible party, you may have just inherited a new task. Management won’t solve a problem that doesn’t cross their radar. If you keep handling the task, it never will. Identify the problem(s) and express the need for additional resources or a more creative solution.
Don’t silently solve additional problems while your own work stacks up. You could become overwhelmed and eventually burn out.