For an oscilloscope, one does not really need to get close to the PC to get good performance. What is difficult to do is the real-time behaviour; interfaces like USB3 have a non-deterministic bandwidth over short time scales because it is a shared bus. Even on a modern CPU, because of the imperfect nature of pipelining/branch prediction, it is difficult to get the real time guarantees that would be needed for a high speed oscilloscope. And then you have to process the data; I would imagine that it would be not too difficult to get an ADC to stream data to your PC at 1-2Gb/s using one of the cypress FX3 boards but it would be very hard to process that information at >1Gb/s.
If you look at the 62GHz agilent oscilloscopes, they "just" have a barebones PC connected to FPGAs via PCI-Express. This trend is the same in basically all DSOs on the market; the FPGAs talk relatively slowly to application processor which draws the pretty menus. Alternatively, some DSOs pass the video signal through FPGA/ASIC so it can replace the pixels on the display area with the waveform information. A general purpose CPU is just not "real-time" enough for this sort of purpose.
As I understand it, interconnect bandwidth is not really the limiting problem in any of these devices; it is in the DAC/ADC and analog performance.