Is it ethical to explicitly or implicitly bias against student papers unless co-authored with senior researcher(s)?
In my opinion, such a policy is absolutely unethical.

One of the key principles of science is that scientific work can be done by anybody.  Good science can be done by people who aren't even in academia, let alone by students.  A scientific paper should be evaluated on its merits, not an argument from authority based on its authors.

Now, humans being humans, reviewers will tend to bias towards known authorities and prejudice against unknowns, students, etc.  But this journal's policy, rather than fighting against such a tendency, explicitly enshrines and adopts it.  Likewise with the informal policies that you describe: anything that amplifies unfairness in judgement rather than de-amplifying it is highly suspect and likely scientifically unethical.

This doesn't mean that one should drop standards.  Rather, it means that one should treat a paper coming from a well-known PI at an august institution with just as much suspicion as one from a student author from a developing-world university you've never heard of before.  Being status-conscious primates, we're not very good at doing this, but such a condition is the goal towards which we should strive.

PS: Note that a policy the other way, i.e., student journals that don't accept papers without student authors, is not problematic because it is inverting the privilege gradient.