I’d say that having three different words for “because” increases nuance. As the link to merriam-webster’s article pointed out, you get a nuance of formality between “because” and “as”; “as” is somewhat more formal. I’m not sure if there’s another nuance between “because” and causal “since” but smart money is on there being one (if you survey the use of the two I bet you will find there are very subtle differences of usage there – there almost always are nuances of difference between supposedly synonymous words, even if they’re only differences like level of formality).