The only exception is in individual combat sports (wrestling or judo, for instance). In those cases, not only is it a safety issue, but the 'penalty' for failing to make weight is just that you have to compete in the next weight class up, not that you or your team are ejected from the competition.
European rowers (and I include British people here) are kind of shocked that the US has lightweight categories at high-school level. I suppose, though, that if people are chasing lucrative scholarships to college lightweight teams that might be an incentive...
Scholarships for men's rowing largely don't exist. There are a few schools with full varsity programs, but not many.
Women's rowing, as a scholarship activity, is a largely new thing - there was a massive increase in women's rowing in the 1990s in order to comply with federal regulations. The men's football (American, not soccer) team has 85 scholarships available - rowing is an easy way to add 20+ women's scholarships.
As for lightweights in high school, I was one. If there was no lightweight program, I likely would have stuck to XC running. No way I could compete against the typical 180lb+ heavyweight at 140lbs.