Much like college tuition increases, a government tax break merely means the suppliers will all increase prices to adsorb the new supply of money. Its basic supply and demand, you have a supply of more money, so we'll demand it. A govt tax break has no impact on the standard of living of the population, its a give away for the industry it applies to.
Also DCRA is a complicated tax mess where its incompatible with some other social engineering child tax credit scheme, causing all manner of annoyance and confusion. That's all I remember of that detail, at least 5 to 10 years ago at the fed level you could put pre-tax income into a DCRA OR not pay income tax on some small subset of childcare expenses but obviously you couldn't double dip and apply both credits to untax your untaxed income although the paperwork made it easy enough to accidentally try.