Not to be obstinate, but I think detonum's answer is still valid.
A. If you can NOT rotate the left forearm to square the clubface, then it helps to switch to a neutral grip in order to LEARN this.
B. If you CAN already rotate the clubface and square it up, then there are a variety of grip options, and you might want to try out what works best for you.
I don't want to speak for Brian, but when you say "I know Brian does not suggest a neutral grip for everyone," I don't think this is because he has a bunch of secret reasons for suggesting grips. That is, I think a lot of times Brian will leave someone's grip alone, if there's not a good reason to change it.
Thus, unless YOU have a good reason to change it, then you might not want to. But if you are searching for the best grip for your best pattern, then you can always experiment.
My personal preference...if you are going to be picking a grip...is Manzella neutral. It forces you to rotate properly, it makes clubface control easier, it makes it easy to work the ball...