An RPi costs about $30. A cheap FPGA Dev board with enough I/O capability to drive a transducer array costs about $300, and requires someone familiar enough with Verilog/VHDL/etc to actually program the thing. I'd guess he's off overall by at least an order of magnitude in any of his cost estimates, even if all the labor is free.

I'm sure such a device can be made much more cheaply than existing solutions, but the author doesn't seem to have a realistic idea of the difficulty.

Also the FPGA is not sufficient. You need something with both power capabilities and a decent freq capability, to drive pulses with some decent energy. On dozen of channels.