As a hobbyist operating system writer, I found that because paging (a major part of the modern protection model) only has a concept of privileged (ring 0,1,2) and unprivileged, the benefit to rings 1 and 2 were diminished greatly.
The intent by Intel in having rings 1 and 2 is for the OS to put device drivers at that level, so they are privileged, but somewhat separated from the rest of the kernel code.
Rings 1 and 2 are in a way, “mostly” privileged. They can access supervisor pages, but if they attempt to use a privileged instruction, they still GPF like ring 3 would. So it is not a bad place for drivers as Intel planned…
That said, they definitely do have use in some designs. In fact, not always directly by the OS. For example, VirtualBox, a Virtual Machine, puts the guest kernel code in ring 1. I am also sure some operating systems do make use of them, I just don’t think it is a popular design at the moment.