This is the big reason other countries have free or cheap childcare. People who have kids want to continue earning money, and people who earn money want to have kids. It can be easily justified using only an economic productivity argument.

Very few other countries have free childcare. In Europe I'm only aware of Slovenia and a couple others. Canada doesn't have anything close to the universal system that's in New Mexico.

In which country there is a cheap childcare, especially if we are talking about children under 3?

Also even if it is cheap, children can attend it few days a week, staying sick at home almost every week for a day or two. Not every employer can tolerate such worker.