There is one potential downside to not having a torn rotator cuff tendon repaired. Over time a number of small partial-thickness rotator cuff tears progress to become large full-thickness tears. Some of these larger tears become painful. If you choose not to have your tear repaired, there is a possibility for the tear to become irreparable.
Despite this, I still feel that rotator cuff surgery should be done to alleviate pain in the shoulder.
Any surgical or invasive procedure carries risks. Before proceeding, you should seek a second opinion from an appropriately qualified health practitioner.