Any product, especially an RF emitter, needs the appropriate certifications before being put on the market, or indeed leave the lab environment, where it can cause interference to other users - especially if it interferes with licensed spectrum. Using a pre-certified RF module exempts you from most of the RF emissions testing, but for example for CE (what I'm familiar with) you still need to prove EMC immunity, ESD etc.
So using pre-certified modules essentially makes your certification process faster and cheaper, but doesn't exempt you from it.
For Bluetooth it's a similar situation, using qualified modules lets you reuse the BT PHY QDID in your product so you only pay the declaration fee, no testing is necessary. But yes you still need to register and pay that fee. More advice here: https://www.bluetooth.com/develop-with-bluetooth/qualification-listing/do-i-need-to-list-qualify-my-product