How important are recommendation letters for doctoral program admission?
Because I do not think it is that common! I agree some professors (especially if they overseas or know you in person) will let you write your own letter, they will read it, sign it and send it. Others will use your document as a draft only. But, the majority do not do that since it is very questionable and unethical! 

Most professors write their own letters. Hence, recommendation letters are still important. Especially in cases where they can express if a student is exceptionally good, or to discuss his contribution in writing papers/proposals or even to discuss why did s/he perform poorly in undergraduate level courses (like me!).