In MIPS's case, intellectual property protection made it possible to compete on designing CPU's rather than designing finished products for those CPU's to go into. It allowed them to focus on chip design rather than fab design or manufacturing. And it allowed them to accumulate something of value in the company itself that could be sold later.
Would CPU's get designed without patents? Of course. But I don't think the sort of beneficial division of labor you see with MIPS and ARM would be possible without some sort of intellectual property protection. When you can't easily transact in something, that forces you to try and move every operation involving that thing under one roof. And it's not hard to make the case that those kinds of monolithic companies are worse for competition than patent litigation.