Until we have evidence one way or the other from an actual doctor, I cannot believe the advice of any doctor was "let it go unhealed and untreated for 9 months".
But in any case, this is what NIH says regarding candidates for surgery vs. non-surgery. I feel it's pretty instructive here.
"Reasons rotator cuff repair may be done include:
You have shoulder pain when you rest or at night, and it has not improved with exercises over 6 - 12 months.
You have a large or complete rotator cuff tear.
You are active and use your shoulder for sports or work.
You have a lot of weakness and are unable to do everyday activities.
Surgery is a good choice for a person whose tear was caused by a recent injury. It is also a good choice when the tendons of the rotator cuff were not already frayed from chronic rotator cuff problems.
Some patients with a partial tear may choose not to have surgery, using rest and exercise instead. The best candidates for this approach are those who have only a partial tear and do not place a lot of demand on their shoulder.
Shoulder pain will improve with this approach.
However, any weakness will not improve, the tear will become larger over time, and you may be limited in the sports or other act ivies you can do.