I think your way of categorizing and qualifying "regional public universities" is limited in sight and likely wrong. "What schools can I easily recall?" really seems to be your litmus. Ignoring smaller private schools seems very self serving. Esp when most of the schools in Iowa are private. And it's almost a 40 40 ratio of private vs public in the US in total. Out of the 5,300 institutions in the USA, there are 1,626 public colleges, 1,687 private nonprofit schools (rest being for profit).
Based on this, Iowa has 39 4 year "higher education" schools. More than Nebraska, SD but less than MO and MN. What state is "W" ?
In 2021, there were 384 institutions of higher education in the state of California.
www.statista.com