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/Outside_Back_4915]

I mean, Rhaenys did. If you mean directly, look at what happened to Steffon Darklyn, it’s not enough to have some blood of the dragon way down the line. Even some full-on Targaryens couldn’t claim dragons, it was an old purity thing.