Definitely not. Many people will develop SLAP lesions from normal use of the shoulder throughout their lives. Many post-mortem studies show that the vast majority of people have labral tears at the time of their death.
So, who should consider having a SLAP lesion fixed? If the surgeon believes that the SLAP lesion is the source of pain during overhead sports, then consideration should be given to fixing the tear. In most cases, SLAP lesions do not cause pain at rest or night, so if you are experiencing this, it means something else is bothering your shoulder. In certain posterior tears (in the back of your shoulder), a cyst will also form in the back of the shoulder. That cyst can put pressure on a nerve (supra-scapular nerve) in the back of the shoulder and that can result occasionally in severe pain or weakness if the nerve damage is significant. In those situations you may need to have the tear fixed to prevent the cyst from growing. We used to open the skin and remove the cysts, but more recent literature has shown that this might not be necessary if the tear is fixed arthroscopically.