Closed-source synthesizers, closed source bootup, closed source loaders, etc. etc. You're pretty much trusting the FPGA software more than any CPU.
That's an ironic comparison to make -- Intel bought Altera in 2015, and AMD is in the process of acquiring Xilinx.
Between the two, though, there's been a lot more work done on open toolchains for Xilinx FPGAs.
What I would find fascinating is to think about languages and OSs for FPGA and try to break loose from the utterly boring C/Unix/68k,x86,MIPS,blah paradigm. Having something turnkey with attachment to various ports and a display would be kind of cool. Maybe that exists already.
I worked on a project with a processor-on-an-FPGA and while it wasn't fast, the video codec in FPGA made it useful. Kind of a neat thing I think.
See the Precursor.