One account, several genuinely different audiences
Parents want practical information: schedules, events, safety updates. Prospective families want a sense of the school's culture and community. Current students want to see themselves and their peers reflected. A content strategy that serves only one of these audiences leaves the others without a reason to follow.
In the US, FERPA shapes what can be posted about a specific student
The Family Educational Rights and Privacy Act (FERPA) protects student education records, and many schools maintain an annual opt-out list: families who have declined to have their child's name or image used publicly, which "directory information" provisions otherwise generally allow schools to share without individual consent each time. A current opt-out list, checked before every post naming or showing a specific student, is what keeps this compliant. A one-time blanket assumption that all families are fine with it does not.
Community and achievement content tends to perform best
A specific student or team achievement, a genuine classroom moment, or a community event earns more engagement than an administrative announcement. The human content is what parents and the wider community want to see and share.
A single account rarely serves every audience equally well
A district or school large enough to have distinct sub-communities (individual schools, specific programs, athletics) often finds a single central account struggles to serve all of them at once, since practical logistics for one family's school get buried under district-wide content. Separate accounts per school or program, cross-linked from a central one, serve each audience better than one account trying to be everything to everyone.