Nintendo gets a bad rap because they're more militant about this than other major publishers. For example, Microsoft is far more lax when it comes to fan creations. While they do have their rules regarding what is or isn't allowed, they have allowed quite a few fan games based on properties like Halo, including SPV3, Installation 01, and Project Contingency. If MS was like Nintendo, they would have shut those projects down on sight.
Nintendo may be within their rights to do what they do, but this zero-tolerance approach to fan games does not built any good will with gamers. They could at least try a more permissive approach like what MS does, allowing non-commercial releases of projects based on Nintendo IP with certain sharply-defined parameters.
This is spot on. It's not about whether Nintendo have the right to do what they do. It's about whether it's the correct thing for them to do. I say it gives them a bad look and hurts their fans.
Sega are the example I always turn to now. The best Sonic game in literally decades came as a result of Sega allowing and even encouraging the fan game and ROM hacking community. This allowed them to spot and hire the super-talented superfans who get what makes a great Sonic game better than Sega's own devs. I imagine Sonic Mania has spun rather a lot of money from Sega (not to mention the Sonic remakes made by the same guys), and contrary to what some people have said in this topic, I haven't noticed that Sega have somehow lost the Sonic IP because they didn't defend it hard enough.