Piazza’s great, but students* are still going to expect you to debrief WebWork questions in class and may get testy when you don’t. So I think you should plan on having some sort of carrot/stick mechanism to make it worth their while. Putting students in charge of giving the explanations is one way to do this.
I don’t know how many students you have or how much WeBWork you give out typically; let’s assume 40 students and 10 problems a week over 14 weeks. You could set up the course grading so that in order to earn an “A” in the course, you have to provide at least three high-quality complete solutions to WeBWorK questions on Piazza during the semester — at least two of which much be on video, working out the solution on the board with your handwriting, voice, and image in the frame at all times (to verify authorship). The third one can be just written up. To get a “B” in the course, do two solutions (one of which must be video) To get a “C” in the course, do one (that must be video). Students who don’t contribute are not eligible for a grade of “C” or higher. (Which is fair.)
Your job in this situation becomes coaching students as they write up or record their explanations. Students can make drafts of video or written solutions and give them to you first (or post them as drafts on Piazza) and then you can just flip the switch to make the post public if you think they are good enough for the class. This way rather than being an answer piñata (a great term if there ever was one) you're helping facilitate a community where students are teaching each other.
Logistically if you have 40 students and 140 WebWork problems then every student has the opportunity to do 3 of them. You can set it up so that students can do no more than one in a given week, so worst-case scenario is that you’d have to review 40 solutions per week which isn’t so bad. The grading is just done on a Good Enough/Needs Revision scale, no point-fussing necessary, and in my experience it’s quite quick to determine whether a solution is Good Enough.
I did something similar to this in an online calculus class (with 20 students so YMMV) and it worked out extremely well. Another thing I did with that class, which you may or may not think is a good idea, is to make the exams open-Piazza, so students can use their community-generated WeBWorK questions while taking exams — that’s a nice incentive to get the job done right.
*Not all of them. Probably not all.