It's not like OP is replacing her entirity with Alexa, if I were the wife I'd think "sure, let's 'backup' my voice, having it available in case I lose mine would be useful, so that people can still hear my thoughts in my voice instead of a robot's."...
> if I were the wife I'd think "sure, let's 'backup' my voice"
That very well seems to be the OP's position as well. That's a far more generous reading of the situation. It makes sense that someone here would have the mindset of "lets keep a backup in case we want access to it later."