I'd be ok with anonymous donations if they were truly anonymous both publicly and to the management of the institution receiving the money.
Maybe this is something that the government could facilitate - pool these resources, then help distribute them where they are needed. Almost like how taxes work.
Maintains uncomfortable eye contact with the camera
This exactly. If you really want to stay anonymous then use a middleman and do it anonymous to the recipient as well.
Everyone involved with the institution, students, parents who pay tuition, teachers, authorities who financially support the institution (...) have a right to know in whose pocket they are.