Can you reuse FCC certification from a pre-certified RF chip and antenna for a new product?
Google "pre-certified chip" and you get a few dozen results, mostly for chip-and-pin payment. An RF chip is not so much pre-certified as tested by the manufacturer to verify that it is capable of meeting certification requirements when paired with the right antenna. A "pre-certified module" will usually have a shielding package that adds to the size, and that also reassures regulators by making it harder to modify the module after purchase.  The same combination of chip and antenna could produce different results depending on connections, orientation, PCB parameters and routing, and if the agencies did not require such changes verified, no one would be selling the modules.

Yes, the module costs more and constrains your design. Below 10,000 units, it is still worthwhile, just to avoid months of delay and many thousands for testing. Any decent module is generally certified in multiple jurisdictions, giving you future flexibility, instead of needing a lab to test separately for each of those.

Many regulators have some form of Declaration of Conformity self-approval program; you are likely to need at least the paperwork for that even with a pre-certified module.