No, I do not believe that surgery is essential, and there are many professional classical dancers who have labral tears who can keep performing and do not get any pain. As the cartilage of the hip joint does not have very many nerve endings it is possible to have a tear in it without pain. Pain usually comes from the inflammation of the tissues around the joint in response to excessive mobility or compression.
In regards to it having the potential to keep tearing, yes, this is a possibility, however, I do not believe that this risk would be reduced following surgery. Any surgical procedure that requires opening the capsule of a joint will have ramifications on the mobility and function of that joint after the fact, so it is something that needs to be carefully considered.
That being said, there are many dancers who have had surgical procedures on their hip and have also returned to a full professional working load and feel much better for it, so this really must be determined on a case by case basis by your treating doctor.
As a general rule of thumb, I only look at surgery as an option if we are unable to get the dancer back performing without pain. It sounds like your daughter has achieved this so I would delay the surgery a little if at all possible.
I hope that this helps!