Being a good programmer has a surprisingly small role in passing programming interviews. And that just says it all, doesn't it? I agree that interviews should test candidates on certain basic skills, including (time/space) complexity analysis. But do you really learn anything by asking the candidate if they can recite the time complexity of a moving window average algorithm (as I was asked to do by an interviewer yes…
Whiteboard coding doesn't necessarily have to involve guessing the algorithm - any whiteboard questions I've asked avoided doing so. On the flip side, my experience with take home projects is that they are much more of a hazing/pressure cooker ritual - at the least, the time pressure of a Google/FB/etc. interview lasts only a half hour. Most will expect candidates to spend a huge amount of time, which many won't have…
As someone who pushed his company to adopt a "take home" assignment for our interview process, it should be perfectly reasonable to reply with "here's my commit history on a project relevant to what you're hiring for."
I much prefer giving (and taking) take home assignments because it lets the interviewer see _what someone will actually produce on the job_. If you can do that without jumping through our specific hoops, great. If not, that's why we have the assignment.
It also at least somewhat ameliorates the pressure cooker of an interview, which many people cope with poorly. It can be hard enough to communicate clearly when all eyes are on you, let alone get your thoughts together and solve a logic problem. If that's actually analogous to your work environment, well...