If you were a good physics student you may not have appreciated just how bad some of the bad students could be.While I can see merit to showing work in my experience it was only done by lazy teachers wanting to ensure you didn't just copy the answer.
The worst I had was a physics teacher who insisted the class couldn't be properly taught in the summer session and spent the whole first class period telling us why we should drop it. The material wasn't a problem, his "show work" requirement was. I kept getting dinged on the homework for not showing enough work--the hardest part was figuring out how to show enough "work" to make him happy. To me, show "work" means writing out what work I actually did. To him it meant spelling out basic algebra that was so simple I didn't think about it--this was a class that had second semester calculus as a prerequisite, at that point simple algebra is not something you think about when the numbers are small. (I have a sneaking suspicion that his graders were looking at volume rather than contents.)
Someone who couldn't handle that level of math wouldn't have passed the prerequisites.