Your doctor is probably wrong that it can’t be improved naturally, but he’s probably right that surgery isn’t a good idea. #1. It would cause you to need reading glasses sooner, and #2. There is always the potential for complications, and with *mild* nearsightedness it isn’t worth that risk.
On the myopia scale, anything better than -3.00 is mild. In practical terms, if you can comfortably do near-work without glasses, your nearsightedness is fairly mild. Personally, I would be very glad to be at -2.50, but I guess you wouldn’t understand that if you haven’t had worse vision.