Just pointing out that the reality is more complicated. The research wasn't "publicly available", rather it was licensed (exclusively) from Stanford. There is legislation that applies to the ownership of federally funded research, e.g.
The research is publicly available. You can go read it right now and learn from it. You're confusing the difference between the research they did being publicly available, and Stanford holding a patent on PageRank.
The paper is publicly available, but we're not allowed to implement the system they designed in their research because it's patented. The cost of developing PageRank was paid for by the government, but the rewards - a Government-granted monopoly on the use of it and all the income from licensing it - went entirely into private hands.
"A patent is not the grant of a right to make or use or sell. It does not, directly or indirectly, imply any such right. It grants only the right to exclude others."
The point is to provide some temporary protection for inventors in exchange for public usage once the patent has expired.
That's the point from the inventor's perspective, yes. If an inventor wanted it publicly available, she'd just publish it. That's generally how science happens. For an inventor, a patent is a way to guarantee ownership of proceeds.
A government, however, doesn't actually care if the inventor gets paid. The government provides a patent office in order to make inventions public. In return, it provides what the inventor wants: a way to defend ownership.
Notice that you cannot patent something without making it publicly available. It's not possible. If exclusion from intellectual property was the only goal, this would not be true. You should be able to register your invention with the government and reference it in court, only divulging its details when the facts of the case demand it.
Is something "publicly available" if you can be sued for using it? That's the case for patented material for the 20 years before it expires.
There's a difference between the details of the invention being known and it being available for use. In the case of Google, it cost them $300M to license the PageRank algorithm because Stanford owns the patent (despite its inner workings being widely known).
To be clear, according to the supreme court, "It grants only the right to exclude others". So it's a misunderstanding to say "The entire point of a patent is to make it publicly available while funneling money to the patent holder". Sure, patents are often used to release details about an invention while making money off it, but that's just one use case. For example, it can just as well be used as an obstacle to slow down competitors.
"To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries;"
I don't see anything about an invention being "publicly available while funneling money to the patent holder". The "exclusive right" part means the invention is legally the property of the inventor. Others can improve on it, but there is no guarantee the public can use the actual invention until the patent expires.
