Why did most US Universities switch to semesters
There are arguments in favor of both semesters and quarters, but these seem to be inconclusive. (In the U.S.:) In fact, in the 1960s and early 1970s, many places were on semesters... but there was a fad of switching to quarters, so many switched. Then, in the 1990s, there was a fad to switch (yes, "back") to semesters.

So it does not seem to be that it was eventually discovered that semesters are better. Nor that quarters are better. Plausibly semesters are easier to administer, since there're fewer registration events per year. 
On the other hand, students seem to like the shorter "marches"...