Are there benefits to having a bid in writing?

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Just a quickie related to my previous post.

Are there any benefits to having a formal offer in writing, even if the seller verbally told the realtor our intended bid was unacceptable?

The realtor we're working with told us today hours before we went to sign our bid paperwork that she ran our bid by the seller verbally and he said no way. So, we didn't sign the paperwork.

But, I anticipate his mind will change due to many factors (available upon request)

So, would it benefit us to insist that our bid get put in writing anyways?