Why do all households have the same maid?

It's probably a way to save on space. For every household you would then need an additional household slot for their maid - it's not practical. The household level is "above" the world level so it wouldn't know to recognise a maid per world.

That’s interesting. So it is this way for all of us then. Good to know.  It seems that the repairmen and women do vary, ie all households calling for repair don’t get the same worker.  And although I don’t have the add-on, I understand butlers can  vary. So I thought it might be possible there was occasional variation in maids too. 

Today, I inadvertently got a new maid for all households in my game. My then-existing maid called for advice on pursuing his dream job; one of my Sims told him to go for it.  Next thing I knew, he’d become a criminal, and all Households had a new maid (they all continue to share this same maid of course, consistent with my original post).