Is there any pedagogically motivated reason to teach quadratic probing?
Yes, you should at least introduce the idea to your students. 

That said, it is also a truism of education that you need not explain every concept at the same level of detail. In this particular case the first couple of paragraphs of the Wikipedia article on the subject is probably enough. A couple of minutes could be well-spent. 

Students need to know that there are a range of solutions to any given problem and that those possible solutions have trade-offs. This is an excellent opportunity to stress that. Linear probing creates bottlenecks in some situations (poor hash functions for example). That can be a problem. Quadratic probing, while more complex, does a bit better. It might be easier to implement than trying to guarantee better hashes over which the programmer may have less control. Even if that particular solution is never used by your students they will encounter such choices in the future. Help them get ready for it. 

By pure serendipity, Eugene Wallingford's blog post just yesterday discusses a related topic. Blog: Jan22-2018, "Same Footage, Different Film"