I don't have my bags in a safe or locked cabinet, and I don't hide them from house cleaners. My house cleaners are not supervised (I tend to go where they are not so we don't get in each other's way). They fold my laundry but don't organize them into my closet, so there's no reason for them to open my closets, but if they did I really wouldn't know unless I walked in on them by accident or if they changed the position of something inside. My closet doors are nontransparent, so they can't see what's inside unless they open it, but I'm pretty sure they've seen my bags lying around at one time or another, never had anything go missing.
My mother also used to leave bags on counters, and her closet has see-through doors, so her house cleaners could definitely see her bags, she has never had bags or jewelry pieces go missing, though there was a time when the house cleaner brought on a male cousin or some other relative, and my mother noticed $200 cash missing from her wallet, which was in her purse, out on the counter. She's not a lady to misplace money, so after that she told her house cleaner that it would be preferable if she didn't bring new people to her house. Other than that one time we haven't had issues.
I think it would be way to tiresome to hide valuables every time the house cleaners came. Vet people thoroughly with interviews and references before allowing them into your private space, if you deem them to be trustworthy, then trust them unless they do something to prove you wrong.
I will say that this is harder to do in China, but I think that's more due to high turn over. Most of the house cleaners my family had in China had to be watched pretty much the whole time they are there, mostly to make sure they don't damage things during cleaning, also to make sure they don't steal.