It wouldn't, but then it shouldn't go to Cersei either. After they killed the Targaryens it really became a free for all. Are there no Baretheon uncles or cousins or anything that would be in line after Robert or his progeny? I know Robert's brothers are both dead without issue.
Like I said, this will need to be addressed almost immediately next season. Robert Baratheon became king because he was Lord of the Stormlands, killed off the Targ Dynasty and made an alliance with House Lannister. Giving him enough support/forces to declare that he was the king without anyone causing much of a fuss about it. He had the added benefit of being best buds with Lord Stark and Lord Arryn. Both of whom had no problem declaring the Vale and the North to his claim. House Tully, through marriage into House Stark also supported his claim.
Cersei has literally none of that. Not one. For the sake of argument, and that it isn't mentioned in the show at all, let's assume the Stormlands and House Baratheon is spent. So they can't really affect anything. Even if they were still around. I highly doubt whoever the current lord of the Stormlands is would declare for House Lannister.
1. House Stark - Hates lannisters. Focused on internal shit at the moment. Would never support House Lannister.
2. House Arryn - Supports House Stark
3. House Tyrel - lol, and has a huge army due to the population of the Reach being the highest in the kingdoms. Supports Dany
4. House Frey - dead. House Tully will likely return to their rightful places as Lord of the Riverlands and never support House Lannister. Will support House Stark.
5. House Martel - openly hates House Lannister -Supports Dany
6. House Targaryen - massive Army. Dragons. Support of multiple other houses.
7. House Greyjoy - One half supports Dany, the other half also supports Dany for his own benefit...
All she has is House Lannister and the Lannister bannermen. Not that she knows it yet I suppose.