The subsidies that are required are offset by the increased labour force participation that occurs as a direct result of said subsidies. Conversely, if the subsidies disappeared, then there's a good chance that many of those currently employed parents would have to make a choice – do I remain in the workforce and pay $1-2k/month for childcare, or do I quit my job and raise my child/children?
I've had relatives that live in Ontario that had to make this choice. Daycare in Toronto is $1600/month, and can be around $2500/month if you have two children. If one of the parents is pulling in $50,000/year (net pay of $38,979), and you have to drop close to $30,000 for childcare, for 2-4 years, is it even worth staying at your job?