I suppose RHEL uses basically the same kernel, with patches that don't alter its interface too substantially. So I presume that a driver in source form, or even partly in binary blob form, should build and work approximately equally well with any stock kernel.
Beside the driver developers apparently using RHEL / CentOS (so on them the drivers are known to work), what am I missing?
No, I think that's exactly the difference; Linux (in)famously has no stable ABI for drivers, and regularly makes changes that break things if you don't recompile against the updated kernel. Part of the value in RHEL was that they froze significantly more ABI surface, which made it possible to write proprietary drivers that would work across at least minor kernel updates without needing to be changed. That won't work on an upstream kernel because upstream doesn't go out of their way to freeze that ABI surface.
Maintaining any kernel modules that are not in the Linux kernel tree is extremely painful.
Almost every new kernel version breaks the older kernel modules, e.g. device drivers, by moving definitions between kernel headers, by adding or deleting function parameters, or by adding or deleting structure members.
Most of these changes are very poorly documented, so anyone who does not follow daily the kernel development is clueless for instance about which values should be put in the new function parameters or new structure members in order to obtain the same behavior as in the previous kernel version.
The kernel developers who make these breaking changes do not bother to write upgrading instructions for the benefit of those who must maintain an out-of-tree device driver, so those may have to waste a lot of time with reading the kernel sources, to discover what must be done to make the old device drivers compatible with a new kernel.
Some vendors also explicitly detail exactly which distro and versions they support ("RHEL or Centos x.y"), so even if you can get things to work on another distro, a vendor can easily deny your support request with the usual BS line: "that configuration is not supported. Switch back to RHEL x.y or SLES and let us know if you can reproduce the issue! La-la-la have a nice day, buh-bye! phone click".