In fact, the patent system comes close. If what you contributed was inventive and new, you get a patent on that slice of what you invented. For someone to commercialize the whole thing, they may need to pay both parties (essentially both parties who had a part to play in the "discovery" will be paid for their work). In many cases like this, the parties have to cross-license each other (pay each other or license each other for their respective patents).
That is actually what the article says.
"An appeals board of the patent office ruled that the gene-editing inventions claimed by the two institutions were separate and do not overlap."
"Ultimately, companies wanting to apply Crispr for use in medicine, agriculture or other fields might need licenses from both the Broad Institute and the University of California, a lawyer for the university said. ..."
The usual result is that no creative applications of the new technology are legal until both patents run out in 20 years.
Or that a foreign nation that didn't accept the patents becomes the only center of innovation and the nation that paid for it becomes a backwater.
One or both of those happened with steam engines, sewing machines, and aeroplanes. Humanity was not better off.
It was narrowly averted in photography, automobiles, and computer software by governments invalidating the pioneer patents in the field for the benefit of mankind.
I hear ya, especially on aeroplanes (it turns out the Wright brothers were kinda jerks). It's such a shame that, due to the current nature of political discourse, it seems that the only two plausible options are (a) artificial and stifling patent monopolies or (b) expropriation by the state.
There seems to be a very sensible, but verboten, middle ground here: government funding of socially beneficial research and, if a significant public benefit can be demonstrated, compulsory state acquisition under the condition that just compensation is given.
That is actually what the article says.
"An appeals board of the patent office ruled that the gene-editing inventions claimed by the two institutions were separate and do not overlap."
"Ultimately, companies wanting to apply Crispr for use in medicine, agriculture or other fields might need licenses from both the Broad Institute and the University of California, a lawyer for the university said. ..."