I am from Austria and yes I am free to send my kid to any public school in the country that will have them. I've even had times in my own childhood where I live

I am from Austria and yes I am free to send my kid to any public school in the country that will have them. I've even had times in my own childhood where I lived in one state, went to school in another and then switched schools twice within a month because I just didn't like the first one I switched to. I've never heard that we have significant overcrowding issues or somesuch - if anywhere then probably in Vienna, but that's just general capital city capacity woes.