It's hard for a private school to compete with in-state tuition, especially when the state school is in a state with lots of talent that can use in-state tuition rates. A half-scholarship to Florida or even Cal-Fullerton leaves a fairly small tab for a home state baseball player compared to half of a ride to Notre Dame. It's one of the reasons Florida, Texas, California, and any states that have reciprocal agreements with them have consistently better baseball programs than the rest of the country. Weather is another reason, but weather is one of the reasons some states have more talent in the first place.
Northern schools live and die on their ability to use their scholarships on good pitchers. Competing is a matter of getting as many of the top pitchers who already live in cold climates and convincing a southerner to pitch up north every once in a while.
Manieri usually had good pitching when he was at ND. Schlage never did, and I'm waiting to see what Aoki does,