Are you arguing from a theoretical or practical standpoint? In practical cases the FPGA products
do solve my first two issues, as the video output path of the emulation goes directly to the display output in the FPGA. Meanwhile in all software-based emulation products, the video output path goes through a normal Linux graphics stack, which tends to be crap (and not getting better with the silly X11 vs. Wayland fight that keeps Linux's graphics stuck in a bad spot).
That's not an inherent limitation of software emulation, no, but for all practical purposes it is as nobody is doing specialized software emulation for a specific set of hardware to bypass the normal OS/graphics stack. It's instead "throw linux on it, and fullscreen an off the shelf emulator"