First, this question begs the question of “Are the Seven Deadly Sins often used in anime?” Full Metal Alchemist and Soul Eater are provided as examples. Both series deal with the concepts of souls, taboos, and consequences of breaking said taboos. It makes sense that in such a storyline, like stories featuring shinigami, you might come across inclusion of the Seven Deadly Sins (a.k.a. capital vices or cardinal sins).
However, a lot of anime which contain the Seven Deadly Sins as a plot element or even as a reference do not immediately come to mind… Whereas if you asked why the Five Elements (Earth, Water, Fire, Wind, Void) are in so many anime, or why Romeo and Juliet, Cinderella, The Four Symbols (Azure Dragon of the East, Vermilion Bird of the South, White Tiger of the West, Black Turtle of the North), the Chinese Zodiac, Journey to the West (Sun Wukong, a.k.a. the Monkey King), vampires, or such themes are in so many anime, I could more easily and quickly form a list of series that contain these recurring themes. So in contrast, the Seven Deadly Sins are not a major, frequently-occuring theme in the corpus of anime and manga.
The second question asked was “Is there a specific reason for this?” Of course it is easier to write a story around a borrowed theme, or to incorporate one to give support to the story you already want to write, or to simply insert one that has a built-in fan base in order to pull in an audience already primed to find it interesting.
However, to answer whether there is a specific reason in regard to its use in anime (as compared to, say, use of it as a literary device in American comic books), we should consider by what means a Japanese mangaka or anime director could have even heard of the concept of Seven Deadly Sins in the first place.
Basic Japanese education does not include mention of anything that touches on religion virtually at all, even in courses such as History or Literature; it is safe to say that over 90% of Japanese university students have not even heard of the Apostle Paul, who remains one of the most famous figures in world history even from the perspective of non-Christians. They do not have a basic literacy regarding the Bible or other religious texts (including Buddhist and Shinto texts). Unless they attended a Catholic high school, they cannot likely name the main strands of Christianity (Roman Catholicism, Eastern Orthodoxy, Oriental Orthodoxy, Protestantism), name the Ten Commandments, name the Beatitudes, or so on. So the chance that they would have received any mention of the Seven Deadly Sins (which is a much later product of Christianity than the New Testament) within their educational career is very low. Academic writing, writing skills, and creative writing are not generally taught in Japanese schools, and Japanese education does not generally highlight recognizing, analyzing, or making use of literary themes, also rendering the chance of exposure to the Seven as simply a literary reference inside of an academic class low.
Since we cannot look to educational institutions as a likely source of knowledge of the Seven, we should consider other possible sources. Christians in Japan make up less than 1% of the population, and of those, some are "in the closet" and do not mention that they are secretly Christian to any of their friends. Thus, it is not likely for a mangaka or anime director to run into the concept of the Seven Deadly Sins or other Christian-related topics of conversation in regular day-to-day life interactions.
It makes more sense for those Japanese who could recite to you a list of what the Seven Deadly Sins are (and I guarantee you, this would be a meager percentage of the population! I cannot even think of a single one of my Japanese friends here in Japan who I imagine could do it [even though I teach in the English department of a high-ranked Japanese national university and am a doctoral candidate in the Religion department at another]), to have heard of it, most likely, from either 1) coming across it in a prior manga or anime or light novel, or 2) reading of it within the sort of Japanese novels considered to be decent, respectable literature by most Japanese (something like Akutagawa Ryuunosuke or Murakami Haruki). If the Seven Deadly Sins are found in modern Japanese literature, that is a prime source that could have spread the concept.
Since most average Japanese adults do not read manga and do not watch anime, if it was primarily spread through either of these two mediums, we’re looking at the demographics who would know of the Seven Deadly Sins as 1) young children and 2) otaku, neither of whom are a majority in an aging society.
Realistically, what we are looking at is that some author or mangaka in recent history found out about the Seven Deadly Sins and thought it would make a nice trope; then, readers of said novel or manga heard of it, then one of them gave it a different spin in his manga, then someone else saw it there and adopted it, and so on.
One specific reason that a Japanese author or mangaka originally latched onto the idea of Seven Deadly Sins might be precisely because it is not common knowledge in Japanese society: it is novel, foreign, and niche. The Bible originates from the Middle East (which still bears the sense of an exotic, far-away place to the Japanese), though, perhaps unfortunately, most of the Japanese conceive of Christianity as “Western.” While the Seven Deadly Sins are most well-known within Roman Catholicism, their origin is not actually Western. The origin dates from before the East/West schism in Christianity and involves Eastern church fathers. Also, there is wide variation among the strains of Christianity (Roman Catholicism, Eastern Orthodoxy, Oriental Orthodoxy, Protestantism’s many branches, indigenous Christianities), not all of which recognize a set of Seven Deadly Sins (some Eastern ones do, some Western ones do not).
To put it simply, the Seven Deadly Sins has a curious, intriguing, "Other" aspect to it from the Japanese perspective. Precisely because it is not familiar or easy to understand gives it a juicy hook. This means the reason for its use in anime is different in nature from the reason/s for its use in works produced in countries that have a history of Christendom where it is commonplace for the average Joe to have at least heard of the Seven Deadly Sins.
The third question asked was “Or is this a reference of them being beyond sin?” I am not clear on what is being asked in this question (What does “them” refer to?), but an additional factor which should be considered is that, in Japanese language, the word used to translate the Greek word for "sin" is 「罪」(tsumi), which commonly refers to crimes. The average Japanese person does not have a conceptualization of any sin that is not criminal/against the law/severe (such as murder or theft). Thus, the more globally-recognized definition of "sin" as something that one could do which is either 1) mild in its effects (laziness, tell a 'white lie,' shove your brother) or 2) internal/an attitude (lust, greed, pride) is not understood as fitting the definition of 「罪」 to the Japanese. (This means that every missionary and pastor in Japan must go to some pains to re-explain the word “sin” to their would-be converts, because most Japanese do not think they have ever committed a sin at all, since they have never done anything that would warrant getting arrested). The Seven are, therefore, not the easiest things for Japanese to conceive of as fitting the definition of what 「罪」 is, since none of them are illegal: wrath, greed, pride, lust, and envy are things you can keep to yourself without affecting others, and sloth and gluttony are looked down upon as personality flaws but not the sort of things you’d need a Savior to rescue you over. Japan is a rather don’t-ask-don’t-tell, do-whatever-you-want-in-the-privacy-of-your-own-home-and-just-don’t-bother-anyone-else-about-it society, so the Seven Deadly Sins are not necessarily things that the average Japanese even considers make a person evil, bad, or guilty: if you lust over your bishoujo dating sim video game or porn, even on your lab computer at university right in front of everybody, or mention that you’re going out to feel up a stranger's breasts for a fee at the hostess club afterward, your labmates don’t think you need to be punished or forgiven.
So we come back to the fact that the content of the Seven Deadly Sins themselves would be viewed as unexpected and even somewhat bizarre, whereby it could become a theme that sticks in subcultures in which having niche knowledge is valued.