But why does a PA38 have a specified fatigue life while a C152 or PA28 doesn't?
Probably for the simple reason that objectively, based upon service experience and condition, it was found to be necessary. Cessna wings are so remarkably over built, and simple in structure and inspectability, that fatigue seems never to have been a concern. I used to fly a Cessna 207 with more than 19,000 airframe hours, which was a perfectly fit and fine plane.
PA-28s were the subject of and AD getting on 30 years now, which required wing spar attachment inspection. I understand that the basis for issuance of that AD was statistically skewed. The resulting inspection effort was widely agreed to be doing more damage, than the "no damage" being reported by the first inspections. I believe that the AD was withdrawn.
Different aircraft types have different structural design philosophies, so you simply have to understand that which applies to your aircraft, and manage it accordingly....