Nobody needs a Computer Science degree. But if you want to be really good, then you need to have a thorough understanding of all parts within a computer. Get a mental model of a computer from the transistor to the hardware architecture to the boot sequence to the memory models to the operating system internals to the virtual machine and garbage collector of your language du jour.

If pieces from the chain are missing you'll be programming by trial and error. And that way you'll never reach your full potential. Could you learn everything on your own? Absolutely. But without the external pressure you'll simply skip on a lot of tough topics because you don't think you need to know them. But you do.