I think so. If a patent is applied for, the method/solution it provides (physically or otherwise) should be reframed and published as the problem to be solved

I think so. If a patent is applied for, the method/solution it provides (physically or otherwise) should be reframed and published as the problem to be solved and have the public polled for whether they agree to pay the cost. For instance, suppose I invent a new battery, but claim that even though it's the same size and weight as a standard 9V battery, it can last for 40 years at full load. The company making the application could suggest a desired length of time for the patent in months. The USPTO then puts the following on their site: "A patent has been applied for on technology to produce 9V batteries of the standard dimensions and weight as existing batteries, but with a mean lifetime of 40 years. The expected cost to produce one such battery at scale is $1.25. The applicant is asking for 480 months (40 yrs) of protection to exclusively sell and/or license this technology. Do you agree to these terms?" Then the public could vote yes or no. Obviously verification of voters of some sort to prevent fraud, etc, would be needed, but the principle is that the company can set an "asking price" to reveal the technology and we could vote on whether we agree to pay. We'd need a sufficient number of votes before a result would be binding, and the company to could decide to reduce their terms to get more votes (not increase). That's just a possible mechanism, lot's of things to tweak, but I don't think it's impossible or even impractical in reality to do such a thing (or at least something in the spirit). The grants are useful as well. I think things like the X Prize are a good potential solution to some of the innovation dilemmas we face now with patents. We could target what the problems we most want solved by offering $$$$ to the person/group who comes up with a solution. If the dollars are large enough, then the public could even ask/expect to receive all the rights to exploit the solution should one be found/submitted. And you are right, the dollars allocated to the incentive (grant or prize) would directly reflect the value society places on it (hopefully).