How does House Targaryen let both of their Valyrian steel swords go missing [spoilers extended]

Like okay fine the first time, Bittersteel took Blackfyre and ran away to Essos but they literally capture him later and try to send him to the wall... where the hell is the sword?? Are they not confiscating it before sending him off to the NW???

Also they're just letting Bloodraven keep the sword when he gets sent to the NW too? Shouldn't it have been taken back so it can go to a proper Targaryen heir.. like idk it might helpful when they have to fight another rebellion in the future.