The GPU on these parts is there mostly for being able to boot into BIOS or OS for debugging. Basically when things go wrong and you want to debug what is broken (remove GPU from machine and see if things work)
For example the 780m you mentioned has 12 cores and newer architecture so is probably something like 10 to 15 times more powerful.
This could be a thing if you're running native Linux but some games only work on Windows which you run in a VM instead of dual booting.
That's wildly not true. Transcoding, gaming, multiple displays, etc. They are often used as any other GPU would be used.
Not at all. I drive a 38" monitor with the iGPU of the 7700X. If you don't game and don't run local AI models it's totally fine.
And... No additional GPU fans.
My 7700X build is so quiet it's nearly silent. I can barely hear it's Noctua NH-12S cooler/fan ramping up when under full load and that's how it should be.