I wonder how common for professors to return scored midterm papers to students when the final is not accumulative? I want to reuse some of the questions next year and also is not willing to spend about 10 minutes class time just for returning the papers (90 students).
In mathematics in the US, as far as I know, I have never known any professor to ever not return midterms. I always do, and everyone else I know does as well.
Seeing their graded midterm gives useful information. It lets students know what they have gotten wrong and what they have gotten right; it also lets them know what answers they thought were "right" but in fact are incomplete or inadequately explained.
I personally believe the downsides are miniscule in comparison to the benefits for the students.
I personally think your students would find it very odd were they not to receive their papers' back. I can imagine a couple of scenarios in which not returning them might cause problems.
Not returning the papers would mean that your students would be unable to see what they got right or wrong. This could be a practical issue for you if some students wish to challenge their grades. If you haven't given them their papers back, then they could argue that your pulling numbers from thin air. Furthermore, even if they aren't going to be tested on the material later, some students may wish to see what they got wrong so that they properly learn the material.
To specifically answer your question, I think that it's incredibly uncommon. I've never encountered such a thing. One thing you might consider re: managing time is to leave the papers in an envelope outside your door, give them to the department admin to be picked up by the students (if the admin is willing to do so), or put them by the door at the end of class.
I would suggest you discuss your idea with your department chair before taking any action.
That being said, I don't necessarily see any problem with keeping the midterms in your possession. In my experience, final exams are never returned to students. If you are not going to test them on the material again, I don't see how a midterm would be different. You should, of course, give students an opportunity to go over their exam with you if they choose.
I am a bit more critical of your plan to recycle questions from year-to-year. It's not that I think you can't ever recycle questions, but it seems to be better policy to have a variety of questions which assess the same skill. This way, you are only reusing questions every few years.
This depends a lot on local practice and rules. In the university (in Spain) where I work, the rules require the professor to keep exams (this includes midterms and similar exams) for at least a year after final grades are assigned. On the other hand, a student has a right to see an exam and to examine how it was scored, but it is not consistent with the rules to give the exam to the student to keep it. A common thing is to return the graded exams and then collect them again. Another is to designate a time and place for students to examine their papers. When I was a student in the US, the practice was similar, at least with respect to final exams. One reason for such a requirement is that, in the event of disagreements about grades (and for other reasons, such as inspection by an acreditation agency), it guarantees the availability of the exams on which the grades are based for examination by a third party.