The best interview is a pair programming session
So once again, we're back to: there is no single best-way to fully assess a candidate.
Even for juniors and new grads, at school people code next to each other all the time.
sitting next to someone while they code
This is a terrible idea. If they come up with a brilliant solution can you actually use this in production? Who owns the code they write during an interview?
The last time I did anything like that was over 10 years ago. How would that skew your hiring process?
I have pair programmed (over 10 years ago) and I never saw any benefit from it. I work in an environment where every line of code checked into the repository is reviewed and documented in agonizing detail (welcome to the wonderful world of Medical Device software!) and I completely fail to see the benefit of pair programming.
But actually creating new code with someone sitting there - that's something that's not something I've seen often