OMG, they very much do. It is not on 100% of the traffic but at any given time a more then smaller % is subject to DPI.

Not anymore and mainland Chinese manufacturers sell them on in large numbers to autocratic governments.

Such devices have a pretty simple architecture: the highly performant data plane where DPI is implemented in the hardware (using either ASIC's or FPGA's – don't have enough information), and the control plane. The control plane comes with a SDK of sorts that DPI appliance users can use to tailor the appliance to their environment and that is used to «refine» the data plane behaviour, i.e. sending down / updating DPI pattern matching / processing rules.