Alternatives include substance and property dualism, and monism such as that put forward by George Berkeley. In the materialist camp, besides identity theory (where mind = brain), there are also non-reductive physicalists, though I think that's a poor alternative.
Although Sean Carroll is a scientist, his claim that mind = body is a philosophical one, not a scientific one. I would not be surprised if most scientists are identity theorists or similar when it comes to these questions, but that's more a product of (a) science community culture and (b) the fact that science covers a group of methods to try to answer questions about the material world. There are questions worth asking, and worth trying to answer, that are not scientific questions and not amenable to investigation via scientific methodologies. Those might be mathematical (is there any rational number that is the square root of two?) or logical (e.g., whether to accept S5 modal logic), or other philosophical questions (does God exist? do the objects of mathematics exist?).
Scientists may find themselves thinking about these question, may have strong opinions about some of them (as indeed Sean Carroll does), but these are not scientific questions. Many of the interesting questions about the relation between mind and body are for now philosophical (with some overlap with science -- e.g., finding out ways in which the brain can affect the mind).
On that point, I don't see the relevance of the fact (if indeed it is a fact) that billions of bodies have disappeared without a mind ever coming back. Suppose that someone thinks that brain and mind are not identical -- why would they expect the mind to come back once the body disappears?