Literally anyone should be eligible to run for US President
More broadly, there is no need to write requirements like this into the Constitution. If the US people want a president with business experience, they can simply vote for the candidate with business experience. The same goes, I think, for the other two notable requirements for the presidency -- age and birthplace. If being old is such a fundamental qualification, then the voters should recognize that and refuse to vote for a young candidate. And if they genuinely think a 29-year-old is the best person for the job, why should the Constitution stop them?
The only legal barriers to candidacy for any elected office should be ones that are necessary to balance out unfair advantages that would allow a candidate to do an end run around the will of the people. For example, a hard rule against people convicted of serious crimes makes sense -- not because the voters can't be trusted to vote out a felon, but because such people have demonstrated the will and means to cheat the system. I think the requirements for legislators to reside in their districts is justifiable on these grounds as well. Residency rules help keep parties from bringing in ringers and deluging the district with resources to get the candidate that's useful to the national party. Nevertheless, the rules should be loose enough that communities aren't prevented from electing an outsider if that's who they genuinely think will represent their interests best.
Hard rules make more sense for controlling conduct once in office and kicking violators out. Elections are rare enough that they can't be fully relied on to discipline officials, and so it makes sense for general qualifications to be written into law rather than left to the voters to weigh in their decisions of who to elect.