The thing that confuses me about this explanation: we already do that. So it doesn't make much sense as a proposed solution to a supposedly new problem.
It seems plausible to me that the new problem (men without partners) is in part due to weakened social as well as legal norms around marriage, but via divorce rather than polygamy. In my opinion that doesn't mean we should go back to the old ways, but it's worth being aware of the connection.