Thanks for sharing your feedback with us, @Stellan_Kristiansson! We already have a thread on this topic so I’ve gone ahead and merged your post with Global Shortcut To Add A New Task to consolidate feedback. We don’t have immediate plans to implement a global shortcut to create tasks, we will update the thread if we have any news in the future.
In the meantime, you can quickly create new tasks typing task.new in your browser: Create a new Asana task from any browser address bar with task.new
I hope this helps!