Edit: This first point was wrong, but the second point still stands.
Polygyny wouldn't solve the aforementioned problem if we suppose that the birth rate of men and women is roughly the same. If one man has many wives, some of whom even die, then several other men won't have any wives.
The birth rate of XY babies is actually slightly higher than XX babies. On the other hand, babies with higher testosterone tend to have weaker immune systems and so are more susceptible to infant mortality from disease.
Otherwise, I’m not sure what the problem is with men who don’t have wives? They simply don’t reproduce. Throughout history men have reproduced at a lower rate than women. In polygynous cultures it’s only the very powerful and wealthy men who have many wives. The poor and powerless men have few or none.
Huh, really? I thought there were slightly more women than men, but maybe that depends on the economies etc.
As for your second point, yes, exactly. They don't reproduce. So it doesn't matter if many men get one wife each, or if a few men get many wives each, the number of pregnancies won't change, and the number of pregnancy-related deaths won't change either. So (again), I don't see how polygyny helps in this situation.
Multiple wives => redundant wives. Solves the issue of mothers dying in pregnancy. The more wives you have, the more you expect to survive to be able to care for the children. Having only one wife, on the other hand, means all your eggs are in one basket (apologies)!
There is no such thing as redundant wives in a total sense.
There's only kidnapped wives, or dead or single men. That's the only way you get a relative surplus. The amount of women remains the same whether you do polygyny or not.