Why say "to be" instead of "it is" or "exists"?
In english there are many alternative ways to say something, differing only in formality, nuance, or emphasis. The same is true of Chinese.
是 is neutral, 為 is more formal/literary, 乃 is an even more formal and literary alternative.
I recommend seeing example uses of vocab to get an idea of what formality or ways it is used. For example the 乃 I just listed can be a formal and literary "is" but you are much more likely to see it used as "therefore" in regular speech.
Compare 為 you will encounter it as "is" in formal speech but usually its "act" definition is more common. It could also be a rhetorical question marker in classical chinese, but that knowledge won't help much with modern mandarin.
I think word use is mainly contextual, and looking at the vocab as its used in a sentence or piece is key. Looking at them as individual terms, especially when they are single character terms, to me at least is not so useful.