It may be infeasible for a number of reasons, but this post makes me wonder whether it'd be worth asking candidates how they'd like to be interviewed, then doing that.
I'm pretty sure most of the people who have problems with where do you see yourself in 5 years, what's your biggest weakness, tell me about a time when things didn't go as planned etc. will have just as big a problem with how you'd like to be interviewed - I know for me the answer for how would you like to be interviewed is honestly I would not like to be interviewed in any way whatsoever.
You can ask that question in writing and with no expectation for an immediate response. Much less terrifying that way.
And you'd ask it like: "Here's a bunch of different options for assessing your skills, which one do you think would showcase your strengths best and fits into your schedule etc? Please take your time to think it over, a reply by next week is fine."
As a related example: a candidate for an onsite interview at Google gets a chaperone for lunch. The lunch companion has no input into the hiring decision. (And the Google hiring process is formalised enough that they really have no input.)
Of course, candidates usually don't 100% believe that and treat lunch as a secret test of character and stay on their toes, just to be safe. That can be very stressful for some people.
(I behaved like that when I was a candidate.)
Similar for the topic at hand: you can't just declare to the candidate that you are going to treat the different forms of assessment you offer as equivalent. You actually have to think of mechanisms to convince them. Lest someone pick a more stressful one than they want for fear of discrimination.
(And there are benefits to the candidates for the interview. For example it's strictly time bounded, so you are not going to obsess and pull an all nighter, because you are afraid that the competition is pulling all nighters.)
