Should sysadmins own security for social media accounts?

I would treat these like any other SaaS application. If IT manages access to company services, social media platforms shouldn't be an exception just because marketing uses them.

IT can own the security controls and access process, while the social team owns the content and decides who needs access. That avoids handing the whole job to one side.

It depends on the company and how responsibilities are divided. Permanent IT ownership isn't the only option. The social team could manage day to day access if they're trained, with a clear process for onboarding, departures, and periodic access reviews.

Whatever you choose, write down who handles each task and how the process survives staff turnover. Training alone may not be enough.

I'd start with the practical risks rather than the job title. Make sure MFA is enabled, company accounts aren't tied to someone's personal address where a business address can be used, and departing staff lose access.

Then check what logging and administrative controls each platform actually offers. If those require a different business tier, that's a decision for the account owner and whoever approves the cost.