A Comprehensive Grammar of the English Language (Quirk et al.) says:
>**The subjunctive and modal auxiliaries in indirect speech**<br>
**14.34** There is no _indirect speech construction for the optative subjunctive
(*cf* 11.39), but when it is used to express a wish the construction with *may*
(with a possible backshift to *might*) is sometimes a near-equivalent:
>>'God *bless* America!' she said.<br>
~ She expressed the wish that God *might bless* America.

In this "near-equivalent", *might* seems to be used to denote the same optative meaning as *may* in *May God bless America!*. Am I right about this?

If so, why would you need such an optative meaning of *might* when you already have the noun "wish", which denotes the optative meaning?

For example, I think it's entirely possible to use *would* instead in the near-equivalent:
>She expressed the wish that God *would bless* America.