Society already funds a lot of scientific research. Some of that funding currently goes to private pockets like Wolfram Research, who license out their proprietary tech under expensive and highly limiting licenses (they're licensed per CPU core, Oracle style), so that scientists can do scientific computing.

As a former Mathematica user, a good part of the core functionality is great and ahead of open source, the rest and especially a lot of me-too functionality added over the years is mediocre at best and beaten by open source, while the ecosystem around it is basically nonexistent thanks to the closed nature, so anything not blessed by Wolfram Research is painful. In open source, say Python, people constantly try to outdo each other in performance, DX, etc.; and whatever you need there's likely one or more libraries for it, which you can inspect to decide for yourself or even extend yourself. With Wolfram, you get what you get in the form of binary blobs.

I would love to see institutions pooling resources to advance open source scientific computing, so that it finally crosses the threshold of open and better (from the current open and sometimes better).

Academic institutions have internal IP scouting monitoring every lab for monetizable research.

On top of that, and often competing with the former, professors are constantly exploring (heavily subsidized with public grants and staffed with free grad students) spin-offs to funnel any commercial potential of their research into their own or their buddie's pockets. It's just like in politics with revolving doors and plushy 'speaking engagements' or 'board seats' galore.

> Some of that funding currently goes to private pockets

Most (all?) of that funding goes to private pockets: researchers work for money, equipment costs money, etc.