If you are filing joint returns, then your spouse's SSN must be included on the return.
While you know that your wife doesn't have any NY-sourced income, the state of NY does not know that. The only way NY can confirm she doesn't have any NY income is if they have her SSN to compare with the various tax documents they receive (e.g. W-2s, 1099s).
Yes, they will "see" any non-NY income she might have, but that is easily removed in the income allocation interview of the NY state return program.