It sounds like you are using progress through the practice questions as a competitive score among some group, given that you are concerned about successful submission through plagiarism. Most people wouldn’t need the check as they are using the problems to help their learning, not to compete with others.
Maybe you should ask for a “plagiarism check” button, to be run as an extra service. Then your competitors can demonstrate their progress is somewhat “honest” (or that they can beat a plagiarism check).
I might consider a proposal for checking for simple duplicates. If I am stuck and want to look at a variety of approaches, it’s a little annoying to open several submissions only to find that they are all actually the same. But basically I don’t think even that is enough of an irritant to ask for new functionality. I’d far rather have improved filtering on the submissions list.