As @user37208 says, most graduate students have no idea how to respond to a request like this. More importantly, I think expecting anyone—graduate student or faculty—to truly engage with a faculty candidate only through their talk is hopelessly naive.
In my department, all faculty interviews include a one-hour meeting with a group of PhD students in the candidate's area. No faculty are allowed in this meeting, so that the students can speak freely, without worrying about whether their advisor likes what they say. Typically the same group of students meets with all candidates in each particular subfield, so that they have some basis for comparison.
After the interview(s), someone on the recuiting committee contacts those specific students to ask for feedback, either by email or (if possible) in a face-to-face meeting, again (if possible) without the advisor present. As with faculty, it's important to ask more detailed questions than "So, what do you think?" For example: How do you think the candidate would be as an advisor? Would you consider becoming their student? How well do you think they would teach? How interesting/strong/deep is their research record? (Yes, at this point the students have read a couple of the candidate's papers.) How interesting/creative/realistic/far-reaching is their research vision? Would they bring new expertise/visibility that the department currently lacks? Did they ask you good questions? Did they seem interested in you and your work, or did they seem bored or distracted?
I almost forgot: It's vital that the recruiting committee actually take the student feedback seriously. If the students have any reason to think that their opinion doesn't actually matter, they'll check out (as they should).
Including the students as first-class participants in the interview significantly increases their engagement with the process; the feedback we get from students is surprisingly insightful. It also does a much better job of showing the faculty candidates that the students are mature, thoughtful, independent, creative, and the like—all the qualities that faculty hope for in their own students—than just taking the word of the faculty. It also provides some training for students who might be going on the academic job market themselves soon.
Yes, this system requires a significant amount of trust in the students.
(But if you don't trust your students, why on earth did you admit them?) It also takes a few years to reach a steady state where the senior students understand the process and can explain it to the junior students.
[I'm the chair of the faculty recruiting committee in a top-5 American computer science department.]