I feel you might be understating this! FPGA's and ASIC's have in fact been in use for decades now, they are very much ingrained into many high end products. Any digital oscilloscope has an FPGA, and has done for a very long time, for example. These are often either used in combination with a CPU for the UI part. The CPU might either be an IC on the PCB or what is quite popular is having the CPU be a synthesised one programmed into the FPGA.
ARM, for example, have a whole architecture specifically designed for optimal FPGA synthesis.
There are a number of relatively cheap SBC's out there with an FPGA too. http://linuxgizmos.com/tiny-sbc-runs-linux-on-xilinx-zynq-ar...
[1]http://www.terasic.com.tw/cgi-bin/page/archive.pl?Language=E...
I suspect these have gone out to "select customers".
In the embedded world they're available and not even super new, the Zynq[1] from Xilinx has been out for a few years. It combines an FPGA fabric with hard ARM CPU core(s).
Intel (through the acquisition of Altera) also has such products, like Stratix[1] which also combines FPGA and ARM. I seem to remember seing some x86+FPGA for embedded applications from Intel, but didn't find it with a quick search.
[1] https://www.xilinx.com/products/silicon-devices/soc/zynq-700... [2] https://www.altera.com/products/soc/portfolio/stratix-10-soc...