That is a question . . . which for academics has long been an imperative, and which may explain in part why academic writing is widely considered off the scales on the Fog Index. Forced to write is like being forced to eat or read.
However, I can recall for years saying to myself, “I don’t care if I ever publish, I write for myself.” And it was true and there was a certain purity and freedom in that early writing that, however unpublishable, I love and treasure. And long for, at times.
So, yes, I encourage you to write without thought to who will publish your work. To feel the process, no, I mean to lose yourself to the practice so much so that you look up and forget where you are, who you are. And you know it’s good.
And then, later, when you have activated this autonomic writing system—where it’s like breath—consider the so-called markets where you might publish and find a readership. Then be prepared for editors with notions, who often know less than you, write less than you, but who are totally necessary and worthy of being listened to. You want to learn to dialogue, to discourse with your writing, so you will have to answer what seem like silly questions about your meaning and intent. And over explain things.
And, if you do it with scorn and cynicism, you will not grow as a writer, you will not advance. But if you take to heart this criticism, you will be irritable and annoyed for a while, but then you will see that there is a way—as with explaining things to children—to keep some purity and make things plain and palatable for an audience with a one-size-fits-all sensibility.
So, no, you won’t perish if you don’t publish. Au contraire, the risk of perishing your greatest thoughts and insights is higher when you start to speak to the tamed masses. But it’s worth the challenge.