So, if parents are barely keeping a roof over their head, you think they shouldn’t have access to free education for their children?
The reason public school was even thought of was because the US realized they needed an educated populace if the people were going to vote (and yes, this came before Catholic immigrants, so it wasn’t the, “let’s keep their fertility years down” case. Even Anglo-Saxon Protestant kids had to go to school until they were sixteen).
If I couldn’t go to public school, that would have been a huge problem when I was younger. I grew up in an expensive state, so just decent living conditions cost a bundle. Education costs even more.
Some public schools are bad. Some Catholic schools are bad. It all depends on how you work it and how much a community actually cares about the education of it’s citizens and future voters.
Actually public schooling has always been founded and established historically to eradicate Catholicism and inculcate secular and Protestant values in children unable to go to Catholic schools. Whether overt or subversively, the devil is there in the details looking for souls.
Catholicism has always opposed schooling without Catholic moral values as fundamentally teaching instead the values of the world and its prince – Satan.
The is very basic – after revolutions, such as in France, destroying and taking over Catholic schooling – or in the USA, founded opposed to Catholic religion - where you can read about some of the history of anti-Catholic use of public schooling
from the Catholic League.
Or you can read the quote from the pope I provided earlier. I think it bears restating actually.

Where Christ is denied, there reigns Hell instead.
Due to the devastated and weak Catholic teaching and culture today many people do not understand very fundamental and basic parts of Church history and teaching, especially when they’re tied to education and what is necessary there – because most people do not have a decent Catholic education, and even the actual Catholic schools have submitted to secular values and standards.
Every child’s education in Christian virtue is the most important and indispensable part of that child’s education. Math takes a back seat to God.
‘Obviously the need of this Christian instruction is accentuated by the decline of our times and morals. It is even more demanded by the existence of those public schools, lacking all religion, where everything holy is ridiculed and scorned. There both teachers’ lips and students’ ears are inclined to godlessness. We are referring to those schools which are unjustly called neutral or lay. In reality, they are nothing more than the stronghold of the powers of darkness.’
Pope St. Pius X, ‘Editae Saepe’