The labor theory of value has always struck me as self-refuting--if a given good is only worth the labor used to produce it, why not conserve the labor? Profit happens if you produce something worth more than the labor you put into it. This is true whether you're producing profit for yourself (a sandwich is worth more to you than conserving the effort it would take to make the sandwich) or whether you're selling your labor to someone else, who in turn uses that labor to produce profit. (As you point out, this might produce more wealth, since manufacturing labor is more productive in a robotic factory than in a back yard.)
It may be more economically sound for socialists to make a moral argument that profit morally belongs to laborers more than it belongs to the capitalists (in the sense of "people who provide capital"). The economic argument seems to fall down.
The same reasoning refutes the moral argument as well.
If the new wealth created is the difference between the value of the inputs and the value of the outputs, then the key factors that determine whether or not wealth is created are the definition of the output, the definition of process by which the inputs are transformed into outputs, and the allocation of resources (including the assumption of risk) necessary to initiate that process. These functions are undertaken by "capitalists" rather than "laborers".
Labor is an essential input, but in your model, it is not at all responsible for the creation of wealth.
It may be more economically sound for socialists to make a moral argument that profit morally belongs to laborers more than it belongs to the capitalists (in the sense of "people who provide capital"). The economic argument seems to fall down.