Singapore imports domestic workers for poor neighbouring countries like the Philippines and Myanmar, which keeps wages very low, on the order of US$450/month, not too far off Christie's inflation-adjusted US$220/month. Even the fully loaded cost with government levies, insurance, food & board etc is on the order of $1000/month, considerably cheaper than most other childcare options, particularly if like most Singaporeans both parents work longer hours.
By comparison, Singapore strictly limits the number of cars on the road, auctioning permits called "Certificates of Entitlement" to the highest bidder and imposing around 100% taxes on the cars themselves. As a result, a plain vanilla Toyota Corolla costs US$120,000 all in. What's more, half of that is the COE cost, which is valid for only 10 years, meaning the value of the car depreciates by around $10,000 every year. Add in petrol, servicing, parking etc, and having a live-in helper to run errands and drop off kids etc starts to look quite affordable in comparison.