That opens a surprisingly large landscape of possible attacks and failure modes. The jsit obvious subset being things that happen when your paid gsuite gets disabled (not paying, abuse report, etc), or the domain lapses or is taken over.
A basic free gmail account is very stable compared to almost any other option. L
somebody of the public profile of Nate Silver presumably can hire IT/network people who know how to securely run authoritative DNS (or hire it out to a highly trusted third party as a service), so they can point the MX anywhere they want, and either do email in-house or hire it out to an email service specialist or big cloud service provider.
The risk of having the gsuite paid services shut off are about the same as any other high dollar value paying customer using gsuite or office365 as an email service.
The question was why not, and the answer was because it's more risky. Why would Nate Silver want to do all the things you correctly listed as options when he can simply use the safer, more simple, free gmail option?
A basic free gmail account is very stable compared to almost any other option. L