The first FPGA was put on the market in 1985 so any patents for a plain matrix setup is likely obsolete many times over (5yrs). So for that part one can just make a simple circuit and duplicate it over and over. It won't be as good as the current topsellers but the point is to make a huge matrix available without the entanglements that currently exists.
As for software there already exist some really serious tries to replicate the existing routing software and that's with a unknown chip layout. Making the same effort for a simple and known layout should be way easier. Besides there are a lot of people prepared to write open source software..
A configurable logic matrix chip without ties to corporate directions and without ties to a specific platform would be of significant benefit in the long run.
Getting anything designed will require a lot of money from someone. I can't imagine being completely free of corporate direction type issues, whatever you think those are. And I think there's enough FPGA and other chip patents to wade through and avoid that it would be a big effort to stay clean. And you could still get sued just for the giggles of it and have to pay for that fight, valid attack or not.
In the time it would take, we could be making interesting cores for existing FPGAs, I think that makes way more sense. I'd rather play with an FPGA Replay or other existing board, improving Minimig and adding new stuff, than spending 3+ years making a chip, debugging it, debugging software, and then start making fun cores and stuff.
I've done silicon layout of FPGA chips. Spent 8 or 9 years doing that in a small team. In that time was two technology generations based on an existing archtecture. I don't know how long it takes to define the architecture and code up RTL of that. I do know it takes a LOT of time just for layout implementation of whatever architecture, and I have an idea of how much the tools cost and how much masks cost, I know it takes a LLLLLLLOOOOOOOOOOOOTTTTTT of money from someone. Others are free to go at it, but I think the big money guys at Xilinx and Altera etc. are way better suited to making FPGA silicon. I can't imagine seeing such a project happen, just because of the money if nothing else.
I'd be interested to see if anyone ever does such a thing, but I expect I'd still prefer Xilinx/Altera big corp chips due to better performance and features.