Hm, I guess I lucked out then. I bought the cheapest motherboard I could find (at the time) for my 3600, an ASRock B450M Pro4. It makes a bunch of annoying beeps, but doesn't stop booting.
Second this. I got an unraid server working headless with an ASRock B450M ITX board (Fatal1ty) but it's still a real pain having to put in a GPU to boot into BIOS. Was hoping this could fix that for me :(
Yeah, it's a real pain in the ass. I miss the workstations of yesteryear where you could do everything with just a serial console. Another example of technology actually getting worse over time.
Even hardware that is made to be run headless ("server-class") is hopelessly broken. They give you a proprietary graphical console that isn't even just a VNC server but has to be accessed with a web browser. And, if the server is more than a few years old, some deprecated, unsupported plugin like Java or .NET will be required. I have an old Dell R710 whose remote console I will never be able to access, because it only works with Java 6 (or so I'm told, I'm certainly never trying that; I wouldn't even know where to begin to try to set that shit up.)