You're thinking of bleeding edge as "new drug that at least shows up in some pop-sci stuff". People working in labs come up with new methods of doing X in situation Y all the time because X and Y can both be crazy specific to a certain line of inquiry. A thousand of those lines of inquiry will likely be explored before anyone outside of their extremely specific area of study notices. Your sampling bias is pretty irrelevant to the process.
As a concrete example, maybe you need to apply a novel algorithm to a high frequency data source (e.g. a single photon counting module). So you need to program an FPGA with a deserializer to do the processing (in lieu of wasting money on a DAQ that can pump data into your computer at a few GHz sampling rate), and only one postdoc understands the algorithm and FPGAs well enough to do it. Does that sound like a crazy, unusual, made-up scenario?
> This is why startups will, sadly, end up beating academic science over time. Because startups are bleeding edge.
Have you seen how hard it is for startups that actually work on bleeding-edge scientific work to take off? Is that not something that Y-Combinator (for example) has specifically been looking for a more hybridized model for? Most research done at university is a very risky bet even for startups, especially if you want not just a result but a marketable result.
Want some concrete examples of the system working? Take a look at the envelope that quantum information research has pushed in the last 5 years. On the theoretical computer science side, you've got people like Scott Aronson answering significant open questions at a dizzying rate (read his blog for some basic, well-explained evidence). Meanwhile you've got groups like Martinis'[1] making the first quantum computer that can accurately simulate a different quantum system. All with a huge amount of collaboration in a social network of scientists that spans the globe.
Where's your evidence that startups are the hammer-screwdriver-impact-driver combo that solves all of humanity's intellectual problems with but one institution? Because that's a much stronger claim than "academia does moonshot research that wouldn't get done otherwise and its not the scientific equivalent of another day another CRUD app".
[1]: http://web.physics.ucsb.edu/~martinisgroup/publications.shtm...