House words in Westeros aren’t just a catchy buzzword. They’re a mantra, an ethos to the way that this family works. Even after she’s Lady Stark, Catelyn Tully Stark makes decisions based on the Tully creed family, duty, honour. Daenerys spends her arc from Pentos to Meereen to the Dothraki Sea again figuring out what it means to bring fire and blood.
So if the Tyrells want to grow strong, work their way up the social chain, into positions of power, and have a Tyrell child one day be King on the Iron Throne… why marry the gay Baratheon brother?
This post could also be titled: the Tyrells knew all about the Lannister twins incest, because Mace’s enthusiasm for a Tyrell King only makes sense if he knew that a child born to Renly Baratheon had the best chance of ending up on the Iron Throne.