The signal is valuable. The unnatural barrier to entry is, at best, unethical.
Ideally, the barrier to the opportunity to earn the credential would not exist. It should be available to everyone worldwide.
Individual research positions should be applied for. Certain practical skills must be taught in labs, etc. But the vast majority of intellectual effort in a Harvard degree should already have all its coursework and testing available to everyone, and at reasonable cost. Otherwise it is not an open competition, it is an institution promoting socioeconomi status.
That may or may not be why some of the elite schools open up their courses but not their accreditation online. It may not be in the institutions best interest to be as open as the ideal you describe.