The term doesn't translate very well to English, especially when you consider it is abbreviated into 3 syllables in Japanese. I didn't mind it one way or the other, but as the others mentioned, I wished they went with localised terms, to keep the subtitles concise.
(full disclosure: I use a different username here, but I coined SHSL oh so many years ago now)
First, it's not 3 syllables in Japanese -- it's technically 8 moras (cho-u-ko-u-ko-u-kyu-u), which is what Japanese uses in lieu of syllables, but I'll give you 4 if you can't hear the difference. "Ultimate" is 3 syllables and "Super High School Level" is 6, so we're all over the place. To my ears, "Super High School Level" fits exactly the same speech pattern as a correct pronunciation of "Choukoukoukyuu", while "Ultimate" sounds way too short.
But that's not even that important. Here's why I defend my translation (or at least a translation in its spirit, I'm not particularly tied to SHSL) over Ultimate. It's basically the same argument for why I'll defend Monobear over Monokuma forever:
Translations, at their best, have to struggle the long spectrum between lexical-accuracy and free-form rewrites in order to achieve the ultimate goal, which is to have the source and target texts have roughly the same feel (while keeping the meaning intact, of course). Those who argue that "Super High School Level" sounds awkward in English are missing an important point - "Choukoukoukyuu" is super-awkward in Japanese too. "Choukoukoukyuu Zetsubou" isn't supposed to be menacing - it's supposed to sound ridiculous.
My guess is that the term was chosen carefully. Dangan Ronpa is, among other things, a comedy and a satire. Choukoukoukyuu is exactly a satirical take on the pompous title a fancy private academy might give its students. The series does the same thing with the name of the Incident - unnecessary long and pompous, and repeated ad nauseam in the dialogue for comedic effect. Add to that the implications of the title - the students are still High School Level (that is, they're *not* the best in the entire world at what they're doing, just among their age group) - but they're *Super* that level! Then, of course, the series likes to play with that - we have the Choushogakkoukyuu (Super Elementary School Level) kids in AE, whose skills are only fit for elementary school, and in this new series everyone is titled Former-SHSL, almost as if to say high school was the highlight of their entire lives (Japan, anyone?) Not to mention that being the best student council president isn't exactly a useful skill post high school.
So, yeah - "Ultimate" is bland, inaccurate, sounds cool instead of ridiculous, and removes the satire from the text. I like a lot of things about NISA's translation, but that's not on one of them.