That's such a terrible option that I totally forgot about it.
It's not just the daily laundry and butt wiping that takes money, it's also medicine and actual medics to treat them. As the number of tax payers to tax receivers shrinks cuts will have to be made everywhere and taxation increased to cover rising costs in spite of inferior service.
Another problem with the robot revolution is that it takes away jobs from people. They will then have to find other work if they can, or go on the public teat further increasing public expenses. Using robots and automation in general instead of real humans also destroys the bonds between people. They become names on a screen instead of real humans, leading to an unemphatic society where people just don't care about eachother because their social interactions are limited. This is already happening in socialist utopias around the world.
And ultimately the real problem is the fertility level. Anything below 2.1 means the country is, in the most literal terms, dying. This is often coupled with massively increased immigration, which will eventually displace the native population. Look to England for fucks sake, they have Sharia courts that are fully legitimate and London has a minority of brits at this point.
What brand of tin foil do you use? ;-)
Firstly, caring as in professionally looking after people is a low wage economy kind of thing - not a job to aspire to so nobody wants to do it. That is where robots kick ass! Otherwise, we should ban pneumatic diggers, and employ hundreds of people to dig holes using spoons if jobs is the only thing that counts!
The irony of your sentence talking about technology destroying the bond between people written on an Internet forum where people chat but never meet in real life is almost beyond words!
Finally, a lower fertility is advancement, and the sign of a mature country. Most European countries have a negative natural population - especially Germany - the most advanced country being Japan. Statistically, we will see the population of the Earth dropping within the next 200 years as we get to a point where we don't need as many people to keep the species going.
The problem of immigration is a different issue for a different forum, although I can totally guarantee that while there are a lot of non British born people in London, they are not the majority and Sharia courts are not legal. In fact a few nut jobs who were trying to set up Sharia areas in East London were jailed a week or so ago for spreading religious hate - The UK may not be Christian like the US, but it certainly isn't for any other religion either! ;-)