There's a few, not quite the same, but bits of pieces of places like this exist. Monopoly driven companies like Google or Microsoft have nice R&D arms, car companies can get involved in weird things. There's the big research universities, who are these days just as commercial as PARC ever was. There's also DoE National Labs who, because of the downturn in the nuke business, get involved in all kinds of cool R&D and are surprising to most people only semi-government. And finally there's pure government R&D centers, mostly in the military.
Control F for national labs, and this is the only comment that came up. That makes me sad.
The DOE and NNSA national labs are enormous R&D institutions and have grown far beyond their original propose in the atomic weapons complex.[1]
I personally work for an office that pumps over 100 million annually into the system, and frankly that's small change. Probably about 40%-60% of that money goes into overhead and facilities which enables research outside of my project.
There are a lot of fair criticisms of the system, but most of that is because real R&D works like ycombinator. Lots of investment, with the hope that eventually something pays off in a huge way. Like the system or not, most people who are unhappy with it are really just unhappy about government sponsored R&D. Almost by definition, it's not going to be "efficient" in the short term.
If people are interested in big money, complex problem science, i encourage you to take a look at the labs. They cover everything from supercomputers, to marine science, to renewable energy.
