If you're experienced in the x86(-64) world, then yes the move to a RISC processor is a good sideways move to keep your mind opening. Your questions are good ones.
Answering your second question: yes, MIPS processors are still in use. They're frequently the processors used in things like routers and other small computing appliances like that. They're also increasingly appearing in small home computing devices in Asian marketplaces (Lemote, for example). What they bring to the table over ARM is a competitive price/performance ratio and 64-bit capabilities. What ARM brings over MIPS is a much better power/performance ratio, if memory serves, and a more flexible set of options in constructing cores. SPARC is very pricey, but, to be fair, very fast. I don't know enough about the other architectures mentioned to make any useful comment. (Well, except Itanium which is basically stillborn tech that's not RISC nor CISC.)
Answering now your first question: the reason that MIPS features so prominently in books is that it is almost a perfect exemplar of a RISC system. It is a small, relatively pure RISC implementation that is easily understood and that illustrates RISC concepts well. For pedagogical purposes it is probably the best real-world architecture to show the nature of RISC, along with its warts. Other processors thought of as RISC (ARM, SPARC, Alpha, etc.) are more pragmatic and complicated, obfuscating RISC concepts with some more CISC-like enhancements for better performance or other benefits.
Finally, to answer your final question: I would recommend learning MIPS for the same reason that I recommend people learning OOP pick up Eiffel, people learning functional pick up Haskell and so on. MIPS is the purest implementation of RISC concepts that's in actual real-world use and you will be forced to contend with the RISC way of thinking and only the RISC way of thinking (for the most part) while you solve your problems with it. This will prepare your mind for the RISC approach and make it easier for you to quickly pick up ARM (my recommended second) or SPARC or any other RISC architecture out there even if you never use MIPS directly. (Although as I pointed out you may actually wind up contending with MIPS anyway.)