Yes, tears of the rotator cuff tendons are extremely common. Recent studies report that approximately 30% of over 60 year olds and 60% of people over the age of 70 will have a tear. As such, after the age of 60, rotator cuff tears may be considered a natural part of ageing. It is also important to note the majority of shoulders with a torn rotator cuff will not be painful.
Any surgical or invasive procedure carries risks. Before proceeding, you should seek a second opinion from an appropriately qualified health practitioner.