False modesty, perhaps. One of those things people say without thinking what they mean. "It's only little-ol'-me; pay no attention to what I say". Why write it, then? Why tell me it's next to worthless after I've read it? I already know that.
The theory that the expression arose because that was at one time the postage required for a letter to the editor seems to me unlikely: what possible mental process could assign a text a monetary value equal to the amount of postage required to send it by mail?
"It may not be worth much, but it's my opinion". Well, I know it's your opinion if you signed it, and why don't you let me be the judge of what it's worth to me and whether I ever want to spend any more of my valuable time reading what you write?
Are you saying I'm an idiot for spending any time reading something so cheap? I don't appreciate that. Do you think potential publishers will not show enough contempt for your writings so that you have to make a start by doing it yourself?
In my opinion it is a silly and unnecessary expression. I recommend its abolition.