I’ve been there … when I wanted to apply at one of the best UX companies of the Netherlands I’ve spent 2 days of each 10+ hours to create my portfolio website (this is for myself of course), they asked me to write a case study to show my skill, did that … another 2 days of each 10+ hours. After that, they were impressed, cool … now they had to check if I was a culture fit. Another 3 days working at their place internal working on a real project for them.
Guess what they said: We need somebody with some more experience … which they could have known up front since I told them and they had seen my cv, portfolio website and application letter.
Never again I will do an assignment since I now have my portfolio website. Just have a good and solid portfolio website which shows how you think and come to solutions. But also give them an alternative if you don’t want to do the assignment. For example that you’re more open to doing a brainstorm for an hour or so (which also shows your process, but also how you work together with others). There is also value in there for you, you can see how the company works and how they think. Now you also can decide if the company is right for you.