Tuition is often subsidized with the expectation that graduates will get a better salary than otherwise, generating more tax income in the long run than the amount of the subsidy. As such, free or heavily subsidized tuition can actually be a great investment for the government.
And yes, from that point of view, the students are the product.
This is true for public universities but does not apply to Harvard, which is not part of the government. Any benefit that Harvard obtains from an increased tax base is incredibly attenuated and not really relevant.
