It's certainly dominated by the blue bloods, but in the last 20 years, here are some of the Final Four participants that I don't consider blue bloods:
1998-Utah, Stanford
1999-Ohio State
2000-Florida, Wisconsin
2003-Marquette
2004-Ga Tech, Okie St
2005-Illinois
2006-George Mason, LSU, Florida
2007-Florida, Georgetown
2008-Memphis
2009-Villanova
2010-Butler, WV
2011-Butler, VCU
2012-Ohio St
2013-Wichita St, Michigan
2014-Florida, Wisconsin
2015-Wisconsin
2016-Villanova, Oklahoma
2017-Gonzaga, Oregon, South Carolina
2018-Villanova, Michigan, Loyola
I'm sure there will be disagreement in who I don't label as a blue blood in basketball, but from that list you can see that unlike in college football, you can be a small school or one with little tradition and make a run. There's zero reason that NEbrasketball has been this bad for so long. You don't need 5 one and dones to be good (look at the current #1 team in the country).