Buy a robot, and pay someone remotely to do your housekeeping for you. The housekeeper could even operate it from their smartphones.
If you can hire a remote operator to control a robot for half of the hourly wage that you would have to pay for someone to show up in-person to perform the same task that's still not anywhere close to economical if the robot also takes 10x as long, even if you ignore the up-front cost of the robot itself.
In order for something like that to make sense the robots would either have to become comparable to humans in the speed at which they are able perform their respective tasks, or the tasks would need to be at least partially automated so that an operator can control multiple robots at once.
The only downside is that you've got a real person in your house, but honestly if that's a hangup then you need to suck it up and just do the work yourself.
(2) no "will the cleaner steal my golden watch / company's data" issue - you can always just replay the video and see exactly what the operator was doing / looking at
(3) ability to hire different people remotely - not just cleaners, but maybe repairmen, doctors, chefs, ...
Slap on a VR system to the bot and I am guessing a lot of chores and stuff can be done remotely.
I would imagine a set of ready made extensions for various works, would be helpful as well.