These flavouring particles don't really make much sense. But the same is true in other languages such as English, in which they don't play such a big role. A related phenomenon in English is the discourse marker just. Just imagine you'd have to explain to a non-native speaker what the function of this word at the beginning of this very sentence is. And what this weird adverbial use (in other contexts synonymous with merely, simply, though in this case they would be a bit clumsy) has to do with the original adjective, which is a synonym of fair, upright, righteous, equitable. By the way, calling it a marker of casualness doesn't describe it too accurately. The word just just gives a sentence a slightly different quality that is very hard to describe; calling this quality casualness is just an approximation.
Well, you know, I mean I guess what happens is basically that such a word is at first used in its original sense, but, like, somewhat insincerely. (Of course I just used well, you know, I mean, basically and like because they are further discourse markers of this type. Basically seems to be a recent one. I didn't learn about it in school and was stunned when I first realised how much the word is used in the UK. Like is even more recent.) Then it becomes a fashion, so the original meaning disappears completely. Through one such process people may have started to use just for indicating recency, and then in another such step it required the casualness sense.
if you use these words you are also communicating how wel you speak the language,. It is a bit like showing off. With or without these words people would understand what you are saying, but by adding and using them you add flavour, maybe even humor. It is like playing with words. Look at me, whow.
yes, this use of "eens" would seem close to "mal" (afeinberg may be better-versed here). It's funny, Van Dale (an expert source) defines as "zonder betekenis" but Wikiwoordenboek defines as "modaal bijwoord dat een uitzondering of een voorstel uitdrukt." which is the better explanation and fits here. So, I don't know if it's necessary, but it's what Dutch often use.
That's how it must have started centuries ago, but nowadays in this sentence, eens almost certainly doesn't have this literal meaning. I guess it has gone through a similar process as English for once, though that is emphatic rather than casual.
Theoretically, once and for once should be exact synonyms. But consider this:
- Come along once.
- Come along for once.
The first sentence has the basic meaning. Clearly it would have been nicer if the speaker had added just to make it sound more casual. You can think of the second sentence as if the speaker wanted to express: "No, I didn't forget to say just. See, I even took the time to add another superfluous word, but one that does not make the sentence sound casual. That's how serious I am!" So it's emphatic rather than casual.
Things might have gone in a different direction in English, too, if the word just hadn't offered itself as a casualty marker. In Dutch, there is no direct equivalent, and eens serves this purpose.
So, your translation certainly wasn't completely wrong, and maybe in some contexts it would be exactly right. (I am not sure because in this area there are subtle differences between Dutch and my native German.) But it's a bit as if you translated "come along for once" to another language using a foreign phrase that has no accusatory overtones whatsoever.