I think the point is that the lunations vary by a couple of days within a year, so you might confuse users by stating a phase is on the wrong day when they are unaware a low accuracy algorithm is being used. But that algorithm probably would be good enough for just drawing an icon, since the differences would be imperceptable.
Honestly, I recommend people use the most accurate algorithm they practically can, even if it's overkill for the given application. This just avoids user confusion when different apps give different answers, even if it's not significant.
E.g., I have ported VSOP87 which gives the position of the moon and planets to sub-arcsecond accuracy to a couple of dozen languages. They are much, much longer than the "snippets", but are not impractical, and users won't notice much difference in application size or computation time. https://github.com/gmiller123456/vsop87-multilang
Honestly, I recommend people use the most accurate algorithm they practically can, even if it's overkill for the given application. This just avoids user confusion when different apps give different answers, even if it's not significant.
E.g., I have ported VSOP87 which gives the position of the moon and planets to sub-arcsecond accuracy to a couple of dozen languages. They are much, much longer than the "snippets", but are not impractical, and users won't notice much difference in application size or computation time. https://github.com/gmiller123456/vsop87-multilang