The two are strongly correlated.

Intelligence is a tool - one that can be put to use against any problem. "Get diverse people to come to the table for compromises" is no exception.

Some character traits that are useful to academics are useful to politicians; others are kinda the opposite of what politicians need.

Intelligence? Problem solving? Understanding statistics? Speaking in front of rooms full of people? Communicating complex ideas clearly? Useful for both jobs.

But an academic can be bookish, shy or haughty. Pursuing your own ideas is actively encouraged. There are arguments - but the main audience for the debates are other academics. They needn't collaborate on research with anyone they don't want to, and when they do collaborate everyone has the same destination in mind even if they disagree about the route to get there. When dealing with students, they've all chosen to be there, passed exams and paid money. The work is mostly low-medium stakes, with time to get important things right. And of course they have excellent job security.

Politicians, though? Gotta love campaigning and talking to voters. Gotta all get together behind the party's national platform. Even colleagues in your party are rivals because everyone wants the top job. 'Debates' all about playing to the audience and getting 3-second soundbites for social media, not engaging with the substance of arguments. No choice in who you collaborate with, including people with deep-seated disagreements about things like tax, debt, spending. Gotta represent voters many of whom hate you. Do well at the job and high stakes things you didn't even do get blamed on you, like train crashes and oil markets getting expensive. Oh, and every 4-5 years you're fired and get to re-apply for your job.

I think we have people who are highly intelligent and still unable to navigate social situations. Neurodivergents are not uncommon in academics.