The reality is that, at least anecdotally, the vast majority of teachers tend to be second income earners. They aren't necessarily the primary providers for the family - particularly in elementary school - and they are more interested in a schedule that allows them to work around their children's school schedule. Which, surprise! Teaching does. So they have the same holidays, etc., and don't tend to be looking for child care due to working when their kids are home. In particular - those three months during the summer that you're talking about.

Even then - those three months "off" are a bit of a misnomer. I know plenty of teachers, particularly newer teachers, who use a lot of that time to work on lesson plans, evaluate what happened the prior year and which learning activities went well and which didn't, etc. My first year teacher daughter is looking forward to some planned curriculum teaming with another teacher in her department this summer - they've already got plans to get together and coordinate some of what they are doing, learn from each other, etc.

I think this is one area that the schools could learn from the LDS church. I don't know if it's still this way - but CES recognized that many of their full-time seminary teachers were struggling financially and would go looking for summer jobs (like many teachers - when the teacher IS the primary breadwinner for the family). So they came up with a plan that they would pay these full-time teachers to work through the summer on preparing lesson plans, gaining additional depth of knowledge through their own study or taking classes, etc. It allowed the teachers to improve their teaching, which benefits the students, and also allowed them to feel like they could make ends meet financially.

Obviously, it would need to be well managed and tracked. But I'd be OK with paying teachers to work through the summer and improve themselves as teachers, get better organized, etc. I don't think EVERY teacher would want to - and some might even want to just do it for 6 of their 12 weeks of summer. But I kind of like the idea.