I don’t know what part of the world you’re in, but in the US, student evaluations of teaching have been standard for at least 30 years, and probably longer (my personal experience begins with my freshman year of college in 1994, but from what I understand, the opportunity to evaluate faculty was one of the things student protestors demanded back in the 1960s, and by the 1980s, administrators had figured out that looking at student evaluation forms was much, much easier than measuring teaching quality in any other way). The degree to which they factor into decisions about hiring, retention, and tenure varies by institution, but most colleges and universities give them at least some weight.
Typically, it works like this: In the old days, instructors distributed pencil-and-paper evaluation forms on the last day of class and then left the room, delegating a student volutneer to collect them and bring them to the administrative office that handles such things. Nowadays, students usually receive a link to the evaluation form through their campus e-mail or the course’s learning management system (a sort of web portal accessible only to students in the class). Either way, there’s typically an array of standardized multiple choice items (for example, “rate, on a scale of one to five, how well the assignments in this course improved your understanding of the subject”), plus some optional space for free-form comments about what the student liked or disliked about the course (and yes, if students choose to respond in detail to the last category of questions, it’s often easy to tell who wrote what, but they only thing they HAVE to respond to are the multiple choice items). The instructor is not given access to the evaluation forms until after final grades have been submitted.
And yes, there are all sorts of problems and biases with this system, not least of which (in addition to the ones you’ve pointed out) is that students often rate instructors up or down for factors that have nothing to do with the quality of their teaching, such as personal charisma or having a foreign accent. Nevertheless, they can be a useful tool if they’re read with an awareness of these potential biases and looked at alongside other evidence, with an eye to patterns rather than giving weight to a single set of comments, which is what a good department chair will do.