I think to add some balancing to the game as well as make base characters not seem so cookie cutter, some professions should have a minimum stat requirement to pick. After all you wouldn’t hire a firefighter with lower than 6 strength or a electrical engineer with lower than 5 intelligence.
Other jobs such as desk jobs might start with a lower than average stat such as a lab worker, to simulate the long amounts of time not doing rigorous physical activity, which would require you needing to spend an extra point in strength if you didn’t want to fall behind in strength scaling.
Rather than an artificial stat requirement, it would make more sense to bundle in some stat bonus/penalties with professions.
Sounds like this is better implemented along with a general fitness/training systeem to simulate your states increasing or decreasing based on your activities. These value´s could than be adjusted at the start to represent your general lifestyle of your character. So a lab worker might start with a increase to intelligence becease he has formal education but a soldier would start with a higher stamina, strength and dex do to being more physically trained before the cataclysm. The lab worker could get the same physical stats as the soldier just by being more physically active and training during the cataclysm and the soldier might get the same increase to intelligence do to learning advanced electronics, programming and chemistry.