Robert never wanted the throne.The throne was open to anyone when they found Jamie sitting on there many years ago
Robert was the face of the rebellion but Jon Arryan was the one who called banners to protect Robert and Ned.
Lord Crakehall asked Jaime if they should proclaim a new king. Left unsaid was a clear implication, asking whether Jaime would proclaim Tywin Lannister, Robert Baratheon, or a member of House Targaryen. Jaime told Crakehall to proclaim whichever king he wished.
Robert did have the best claim though
This is Renly from Clash of Kings talking to Ned:
Tell me, what right did my brother Robert ever have to the Iron Throne? Oh, there was talk of blood ties between Baratheon and Targaryen, of weddings a hundred years past, of second sons and elder daughters. No one but the maesters care about any of it. Robert won the throne with his warhammer.
Now obviously that quote addresses both sides of what we're saying and I even agree that at this point might is right, but you also have to look at the source. Renly's trying to justify what he's about to do (going for the throne despite not being next in line) yet he even admits Robert's Baratheon blood came into play and that the maesters (the ones in charge of keeping a documented history) are the ones wo really care.
Plus, Robert was literally the next in line. The Targs were wiped out, besides Viserys and Dany (and even then no one knew where they were), so Robert was literally the next in line with Targaryen blood.
But at the end of the day it's whoever busts their gun who'll get the throne
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