That is one of the hp 1200 features. "Instant printing" means no possibility of turning the printer off. If you unplugged the printer, you would have to wait for it to warm up for 20-30 seconds before you can print (like the vast majority of laser printers). Is the green light annoying or are you bothered by the wasted electricity?
You have the same thing with your TV set at home, it is never truly turned off (just the sound and video are muted). Otherwise your TV set would require 30 seconds to warm up like the old ones did 20+ years ago...