This applies to many things, including deciding to mow your own lawn instead of outsourcing it. Most people think that their time is worth x, and the yard-guy costs y, and if x>y, they should outsource the mowing. It's not as simple as that, as most people cannot earn X on demand - their total hours are capped by law or arrangement. Additionally, people mistakenly use their gross over net pay to calculate it, and then discount the time needed to arrange, inspect and pay.

The ideal childcare arrangement is bartered, such as an agreement between two families to cover childcare with each other. This takes into consideration attachment of the child to the caregivers.

However, it is more efficient economically to have as many children under a single caregiver, as that frees other adults to create value for society (work with me and imagine every job adds value).

Taxation on that arrangement is just the government capturing some of the value created by it becoming more efficient. I don't necessarily have a problem with that, but the childcare company paying tax, paying payroll tax and then the individual employees paying income tax and the owners paying income tax is taxing the activity too many times.