the avoidance of patent/copyright is critical for (legally) having students design their own chips. MIPS was pretty good (and widely used) for teaching assembly, but pretty bad for teaching a class where students design chips
MIPS patents have long expired too (and incidentally for any other CPU released prior to 2006), so that's a moot point.
This is largely contradicted by the (pre RISC-V) MIPS editions of Patterson & Hennessy, Harris & Harris, etc., which teach you how to design a MIPS datapath (at the gate level.)
Regarding silicon implementations, consider that 1) you can synthesize it from HDL/RTL designs using modern CAD tools, and 2) MIPS was originally designed to be simple enough for grad students to implement with the primitive CAD tools of the 1980s (basically semi-manual layout).