No, because a quote can contain a sub-sentence. The period adds meaning to the sentence by adding finality.
"You are going" has a very different meaning from "You are going.", because the first implies there is something `you` are going to do. Whilst the second implies you are being ordered to leave.
In that case, not capitalizing the word immediately following the quote will work as an indicator that the period is not part of the parent. This doesn't work in the case that the word following is a proper noun. But that's an edge case on something that doesn't really matter.
I agree that maintaining punctuation of the quote is important for context. But outside of the quote, it practically never matters if there is a period or not after the quote. The reader may choose.
> He looks up, "This is it." Bob says, gazing at the sky.