If anything, Gendry has a better blood claim to the Iron Throne.
She’s not the rightful heir to anything since the Targaryens lost the throne, which they originally took by conquest themselves.
Dany has gotten as far as she has because of dragons.
I’ve never been her biggest fan due to her fallback move of threatening to roast people if they don’t give her her way, and her argument for why she should rule the Seven Kingdoms is flawed.