It's a process that I don't have conscious control over.

I don't choose to think random thoughts they appear.

Which is different than thoughts I consciously choose to think and engage with.

From my subjective perspective it is an input into my field of awareness.

Your subjective experience is only the tip of the iceberg of your entire brain activity. The conscious part is merely a tool your brain uses to help it achieve its goals, there's no inherent reason to favor it.