The more I teach, the more I believe that giving students a choice on evaluations is a good thing. By this I mean, letting them choose the level of difficulty of a question in order to show me as much as they can.
For example, I could ask students to come up with the equation of a parabolic arch, in multiple forms, given certain parameters. They must then decide elements that will make their solutions easier or more complex. Where should I place the axes? Do I want the zeros to be integers? Do I want the 'a' value of the quadratic to be an integer? Students can choose to make their question more difficult and demonstrate a greater understanding of the curriculum expectations. Students who are still learning and not as solid in their understanding can set the bar a little lower, yet still show a lot of good math.
The argument I hear against this doesn't come from students, it comes from teachers. There is no answer key. Every paper is different. However, tools like Desmos make life much easier when I am marking these types of questions. I feel that technology makes these questions manageable from a busy teacher perspective, but also makes these questions essential as they can't be Googled. I also feel that I am not limiting any of my students (some go way above and beyond my expectations, which is really cool), nor am I making it such that a student doesn't have an entry point.