I think many of the people on HN that say they won't do a take-home assignment would actually do a 30-60 minute take-home assignment if it meant avoiding the "code some algorithm on a whiteboard while the interviewer glares at you" situation. Then on the on-site, you can focus on the design/behavioral type things appropriate to the role's level of seniority.

Also, if you give the same assignment to multiple candidates, you'll get a better sense of how people use different approaches to solving a problem. You can still use discussions around side-projects to complement the process, but having a standard approach for all candidates is helpful.