If I look hard enough, I can find a study that ranks New Mexico at every single ranking from 50th to 1st.
In particular, the study you linked ranks on a lot of factors outside the control of the school - which is largely affected by the huge number of poor people in New Mexico (#1 in the country... Which is why they got the rating they did).
New Mexico is filled with poor people, news at 11. But seriously, a lot of things go into your state's education outcomes: state of the kids coming into the system is actually very important, as is parent participation, before we even get to funding by the state. As the only poor blue state, New Mexico has a lot to make up for, and it can't just magic its problems away.
https://www.aecf.org/interactive/databook?l=35
You can research for yourself and see other evidence that the educational outcomes for children in New Mexico is generally very, very poor.
Expect similar results with New Mexico's "universal" child care.