AMI sells a bmc software stack, https://www.ami.com/megarac/ Intel and small manufacturer were unhappy, about always paying the ami tax. So intel created openbmc, as a hedge against ami's monopoly for small manufacturers. I have heard Openbmc has user from facebook, google, ibm, bytdance, and ali.
Dell owns their own stack in idrac, I have heard most of their systems are nuvoton based. I am suspect dell pays some big bucks to keep their systems at feature parity with the other options, and they view it as a an investment.
There are also silicon devices on the motherboard, that have drivers that are not able to be shared. So it not surprising that companies don't share source in a way that would be useful.
If you wanted a system that as a bmc that could be tested try the asrock-e3c246d4c, it looks like there are hobbyist, that have it running coreboot, and openbmc. (impressively)
https://github.com/AspeedTech-BMC/openbmc (or see the upstream OpenBMC tree)
HPE are adding some OpenBMC support https://www.hpe.com/us/en/compute/openbmc-proliant-servers.h...
This work from Supermicro looked promising https://lore.kernel.org/openbmc/CACPK8XdE0sRmt4x54YJVJO2wDT5...
I agree with you that you should be able to run whatever since in the end it’s just another computer, but the manufacturers believe otherwise since there’s “valuable IP” or whatever (insert rollseyes emoji here).
There are open specs like redfish but still doesn’t get to the heart of the matter.