One mention is enough. The Gemara in Brachos is not ‘the closest.’ It is it, albeit it was said by a non-Jew. If you would see other Pesukim used then you can have a Kasha why did this one outlast them. But the fact that the Rambam didn’t find it necessary to mention the Pasuk is not a Kasha.
And, Chazal use Pesukim this way often. It is not even a Drasha. It is paying attention the particular phrase. If the Torah is telling you to watch yourself dearly lest you do something wrong, we do see from the phrasing that watching yourself is important.