My home server simply serves files to the local network so I don't have experience in what I'm about to say, but I know Plex people often like to have a GPU for transcoding content to a format more suited to streaming after they download it.

My view is that you need a GPU somewhere or the system won't boot, but if you need actual GPU compute then integrated graphics just won't cut it, quick sync or not. I recommend having an integrated GPU in general as they're usually not that much more expensive and don't use a PCIe slot, and of course that's one less part than can fail.

If you're hosting for yourself only I don't think you need an external GPU at all unless you want to do machine learning tasks.