Potential customers for an app like this don't neatly segment into "...folks who are learning Korean..." and "...super-casuals who just want a ballpark representation...". There is a continuum, and the continuum is weighted towards the casual side. Honestly, if most people only learn a little Korean from this app and it broadens their world only a little bit, it's still done tremendous good. Most people are not going to learn Korean, Japanese, Chinese, &c, &c.

I don't think you'll be able to find empirical support for the idea that romanization is unhelpful after the first week of someone's taking up Hangul in a serious way; or for the idea that Hangul is as simple as Hiragana.

Many people say things like this -- "two days to get the basics" and "a week or less to be...comfortable" -- but I doubt there is any empirical support for figures like that. I suspect that a review of the literature will show that people are still referring back to the romanization for the first two years of their studies, across a wide array of language families, if their first language uses the Roman alphabet.

Hebrew has vowel marks. They are little used but they are very helpful, as well.