$student =~ tr/ *//d;
Yes, that will get rid of all the asterisks in the student answer. This will have the side-effect of making some correct answers incorrect and some incorrect answers correct, as I describe above. I think this is asking for trouble.
I would like to train my students through WebWork problems to use the same proper notation and steps to show their clear work (and answers) as I would expect on paper.
I don't think WeBWorK is particularly well suited to that goal. But you have to do what you think is best.