Agreed, but I wouldn't rule out the possibility that a crazy individual with sufficient hardware and software signal processing experience could make it work, where "work" allows for a significant tradeoff or two compared to a modern commercial machine.
DAC is probably the easy part -- use a LFSR and maybe some jellybean filters to get spectral content where you need it. 10MHz is slow enough that you could probably phase it in software if you handwrote everything in bare-metal assembly, paid attention to interrupts and DRAM, etc, etc. At first I thought you'd need a coprocessor (and in that case it might as well be a proper Spartan 6) but perhaps it can be done with a dedicated core. ADC is the probably the harder part. You can't kick the can down the road anymore. Both cost and value are tightly coupled to 2^(bit depth)*(sample rate). If you try to make a shitty ADC out of GPIO pins, you just wind up with a shitty ADC, you can't really hide the flaws and play up the strengths like you did with the DAC.
Or maybe I had it backwards and you could use a good DAC and some sort of sigma-delta like trick to make the shitty GPIO - ADC work.
Fun stuff to think about, but I suspect the real innovation will happen when someone in hardware realizes that DAC/ADC/FPGA technology has slowly and surely advanced far enough that they can do to the ultrasound market what the DS1054Z did to the oscilloscope market.