My general philosophy about this kind of thing is that a potential employer is free to conduct the interviews in whatever way they wish. How they choose to conduct them tells me something important about the company.
If they want to do something that I am just unwilling to do (such as a take-home exercise), I'll say that outright and offer a different way they can gather the information they want. If that's not acceptable to them, then I have a decision to make: is this really a company I want to work for enough to do it anyway? If so, I shut up and do it. If not, then the interview is effectively over.
But I have always had (even when green) an attitude about interviews. I'm not looking at them as the company evaluating me, I'm looking at them as me evaluating the company.
If I had one... I'd probably do it, rather than refuse. Why not? But I might also consider it in my evaluation of the company. (Remember that you're interviewing them, too...)
I did pass one interview out of sheer luck. Small startup, their core person left and they had a tight deadline (i.e. waterfall). CTO asked me my opinion on architectures and stuff, I pulled out my laptop which was covering a lecture on architecture I was doing at that time. He was impressed, we agreed on culture and pay and stuff, and they offered the job the next day. One hour interview.
Interviews are two way though, and you should always evaluate that they have a competent team if they let you skip the coding interviews.
I’ve had many interviews where they ask me to write out a fizzbuzz or something but that takes a few minutes. And I’ve never minded doing that.
If someone gave be a big take home, and I wanted the job, I’d probably just do it.
I currently give a small take home assignment to applicants that I designed to take 15 minutes. Few refuse. If someone proposed an alternative, I’d listen as I’m really just looking to filter out people who can’t code at all (a surprisingly large number of people).
Maybe this changes at 20+ years of experience, but I haven't gotten that impression from my professional network.
If the company thinks inverting a binary tree is the best way to test my capabilities on a completely unrelated job, that reflects poorly on them. They might as well do a push up contest.