RIT/WPI have overlapping liberal builder culture for STEM kids… RPI is, to a great extent, too though more theory-based classes probably. (MIT has a similar overlap). Also all have SUPER nerdy clubs. model trains, ham radio, lots of cos-play and robots, and extra-nerdy frats. There are overlapping subcultures.
Northeastern/RIT/Stevens (and to an extent WPI) has the coop - pre-pro overlapping sub-cultures. I know less about Purdue/Rose… But Rose clearly has the same size vibe and a builder culture no?… Our kids ruled out in geography and more conservative/neutral schools. Mine seems very builder-y too, like WPI/RIT.. Purdue is probably outlier due to sports, but i suspect a huge subset of kids who would thrive at RIT/Stevens/Mines too.
Flagships, you are right is due to solid stem programs, but lots of kids hide in engineering 