A Comprehensive Grammar of the English Language (Quirk et al.) says:

The subjunctive and modal auxiliaries in indirect speech
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.
~ 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.

A Comprehensive Grammar of the English Language (Quirk et al.) says:

14.34 The subjunctive and modal auxiliaries in indirect speech
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.
~ 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.