Quoted " But why IGFx primary is necessary to get all video outputs to work after boot is unclear. If PCIE is set to primary, the motherboard video does not work unless I connect the hdmi cable to the motherboard hdmi after boot."

 If you set ' Primary video output' to PCIE. Then the Primary VGA OR VIDEO makes the  GPU 4090 becomes the primary output source for signal to monitors. And is initialized first before any on board video that the mother board may or may not have installed as per chip set. Since the Crosshair X670E Extreme is capable of using the USB C Ports to output video that is why there is the choice of igfx or PCIe. IF you look into the Windows Device manager you should see two Display adaptors for the Crosshair Extreme the Nvidia RTX 4090 and a AMD Radeon Graphics. I have mine set to the PCIe setting in bios because the RTX 4090 is capable of operating 4 monitors by itself according to specs. There are three DP 1.4 ports and two HDMI  with one other port for VR usage. If you are not using the DP you are leaving performance on the table unused.  I am pushing two 32 inch  2560x1440 at 165hz monitors with DP and have yet to tax the GPU according to the Thor Power supply read out I have yet to draw more than 389 watts while gaming.