All good questions. It's true "USCIS instructions say it's not necessary to include his wife's income". That is true. What's important to understand though is that USCIS doesn't issue visas. Consulates do. It's also important to understand that the I-864 is not just a document to show somebody "qualifies". Just as important, if not more, is that it is a binding contract. Consular officers tend to request that married couple filing joint tax returns, both sign the contract. That's what the I-864a is for, even if the spouse has not income or it's not needed.
Once a Consular Officer requests it, then suddenly it IS required, and not having it there will delay the visa. It is "best practice" to include the I-864a in this situation.
Curious why you mentioned including mom's SS statement, considering what you say above.