There is a difference between a tax break and recognizing something as an expense. The difference is, roughly, the difference between trying to incentivize certain behavior and trying to properly define income (as distinguished from revenue).

E.g. if you're in a business, you get to deduct the cost of employee salaries. The portion of your revenue that goes to employee salaries isn't a benefit to you in any way except as a necessary part of your business. If you didn't have the business, you wouldn't have that expense. Allowing the deduction isn't a "tax break" but is rather necessary in order to properly define "net income" as distinct from "revenue."

Day care is similar. It's a necessary expense of going to work. The portion of your salary spent on daycare isn't a benefit to you in anyway except as a necessary condition of going to work. If you didn't go to work, you wouldn't have that expense.

$100/week. That's $2.50 an hour. An appropriate ratio of caregiver to babies is 3:1. So $7.50 an hour per caregiver. Assume overhead of 33%. That's being generous: I'm going to want to choose a location with a good sized yard so my kids can play outside a lot, and yards cost money. So by my math, that works out to $5 an hour for a caregiver. WTF?

Sure, the ratios can get quite a bit better as the babies get older, but you're still talking about rates that seem more appropriate for the 3rd world or the 19th century with a servant underclass than about rates that are appropriate for the professionals that many early childhood educators are.

I think your numbers might be outdated, we're paying ~1200/mo in a fairly rural area outside of the baltimore area (not exactly known for wealth) for the cheapest "professional" daycare for about 4h a day, as the child is in kindergarden and only needs 3-4 hours a day of extra help. I'm told that the upper end daycare (across the street) is more like 4-5k/mo in the same semi-rural area.