The advantages of NOT using a BT adapter receiver and having a real BT/ANC headphone is that with a BT/ANC headphone you don't need a cable at all -- with the adapter you still need a cable that is going from the headphone or earphone to the adapter, so you have 3 objects (the headphone/IEM, the cable and the adapter).
With a BT/ANC headphone you have all the playback controls in the headphone so you don't need putting an adapter in your shirt, jacket, pocket or similar, and maybe even sometimes worrying about the cable. Using the playback controls from the adpater is ok or not so great depending on type of adapter and the location of this. If you have a BT/ANC headphone, the playback controls are on the headphone, always in the same position. I'm a person that is changing volume ALL the time (and tracks, too, but less constantly) and this feature, with good implementation, is absolutely critical for me -- in my long experience with many BT/ANC headphones, the iO-12 and H95 offer the best user experience for playback controls (the iO-12 have clearly superior sound quality than the H95).
With a BT/ANC headphone you have very more battery life (20-70 hrs depending on the model) from one single charge, and with ANC headphones you also have active noise cancellation (ANC) and transparency modes. Because BT/ANC headphones have a very more big battery, the battery can lasting many years (5 or 10 years or more) without needing replacement or even losing capacity; and some companies, like T+A and Dali, offer replacing the battery service (for a price) when a new battery is necessary.