there are many reasons. testing in house meaning within the pharma corporation...
i can tell you haven't done you're research.
After approving a vaccine, FDA continues to oversee its production to ensure continuing safety. Monitoring of the vaccine and of production activities, including periodic facility inspections, must continue as long as the manufacturer holds a license for the vaccine product.
FDA can require a manufacturer submit the results of their own tests for potency, safety, and purity for each vaccine lot. FDA can require each manufacturer submit samples of each vaccine lot for testing.
Notice it says 'can' not it already is a requirement.
And on the same page it mentions that the FDA follows up with vaccine reactions and effects too (VAERS). Which barely touches on the legal requirements for pharma companies once reactions are found.