Public universities are non-profits so technically charities, yes. Many of the things that faculty and students and staff do for free or for credit or for some other incentive are jobs.
Things you might dismiss as “spec work” are the bread and butter of universities. For example, faculty and grad students spend months putting together and submitting grant proposals which have a tiny chance of being funded. This is in addition to, not part of, regular duties, except that grant seeking is considered a normal part of the profession.
There is nothing special about logo design, it is another task that an organization can choose to do in-house or outsource, and if they choose to do it in-house they can select using their own practice the fraction of the community that gets to try for the job, and how the individuals will be selected.
I wouldn’t suggest anything different. If a campus decides to have their logo designed in-house, it should be voluntary (or perhaps connected to a job for which a staff member was hired) and done by institutional members (students, staff, or faculty).
