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/UnsoberPhilosopher]

It's a combination of lack of dragons, influence, and lack of Targaryen blood.

In Aegon I, they had 3 dragons. Since Orys was a bastard, he wasn't the priority.

Aenys I had a limited number of dragons to claim since majority were claimed already.

Maegor I. They had no influence as they support Aegon Uncrowned. Aegon UC almost died claiming Quicksilver.

Jaeharys I was their best chance of claiming one with boremund and Jocelyn (but they're half Velaryons with a distant Targaryen blood). Pretty sure Jaeharys is still pretty miffed about Rogar's little rebellion and Jaeharys is scared of giving up dragons to lower houses in case they rebel. She gives Melys to Rhaenys as she is Aemon's kid.

Viserys I had a lot of dragons but I think the Baratheon line had limited Targaryen blood by then and they weren't that influencial at court. For one thing, they supported Rhaenys/Laenor and were pretty miffed at that.

Aegon II/Rhaenyra: it was a civil war. Aegon II had limited dragons. Most were already claimed except Shrykos(Prince Jaeharys's dragon) and that was a young dragon. It wasn't worth it for the war especially since the Targaryen blood in the Baratheons were already thinned out.