They are also great in demonstrating knowledge in a new field. For example, if you do C# at your day job but you want to move into Go. Showcasing side projects can demonstrate some experience. This helps sidestep the "well, I don't have Go experience" issue.
This -- exactly. I know of at least one person who's done this and a few others who were able to move into areas of their preferred language (i.e. going from a job that was mainly web/C#/MVC to mainly REST/C#/Angular or React) by doing this.
Even within a larger organization it's possible to use side-project examples as a demonstration that you're ready to move from a team that uses one discipline/language to an unrelated team. While a large organization might be willing to move a senior developer who's a less-perfect-fit from a different department if they've demonstrated that they can be trained/learn what they need to know, it's a lot easier if they can demonstrate that they're a lot more than a "less-than-perfect fit"
