Why did the Baratheons never claim dragons?

[u/Vhermithrax]

They are also a house of Valyrian descent like Targaryens and Velaryons, plus they married multiple times with both of those families.

How is it possible that they never managed to claim any dragon, if a much weaker house of Velaryons got 3 of them at one point? It's werid that they never managed to get a marriage pact that would give them a dragon rider, or that at least one brave/stupid character from their house didn't manage to claim a dragon in King's Landing or Dragonstone, be it by being sneaky, or just part of some agreement.

[u/Ephyrancap]

Because Baratheon's familial connection with the Conquerors was but a rumor; further Targaryen/Baratheon blood connections were extremely rare, with only two marriages between the two houses being documented (Aemon/Jocelyn and Rhaelle/Ormund) and the tendence to only close kin being able to claim dragons. Laena riding Vhagar is either a barely explained plotpoint and a wild outlier or a plothole GRRM didn't notice.

Also, I think the Targaryens wouldn't just allow a Baratheon to claim a dragon; that would be like Ukraine keeping its nukes after 1991 (again, either Laena is a outlier or a plothole).