It isn't hard to create an "ARM compatible" processor, but you can certainly not sell it as this without infringing a trademark (and copyright on the instruction set, etc).

With WiMax and similars, again it's not only patents, but also trademarks that are only licensed to companies that pay the fee and usually have to pass a compliance test as well.

Sure, patents are present but they're only part of the story.

Also, patents are not the only way to protect an invention, the two other common methods are secrecy and publishing it (which prevents anyone else from getting a patent on it)