Pure Good? Pure Evil?

I was wondering, are there situations where setting up a Pure Good and a Pure Evil make sense? What purpose could it have?

I guess it depends on what you mean by "pure". I'll answer based on what I think you mean.

Personally I find such characters really boring because there's no room for them to develop. There's no struggle against their ideals. Even if you're talking about metaphysical kind of beings like gods it doesn't lead to very interesting story-telling. On top of that, a good being would quickly be taken advantage of and abused relentlessly. Also, evil isn't born, it's made. Characters that exist simply to embody an attribute are kids' stuff. I suppose you could use them in a serious setting but you'd have to be very careful with how you handle such characters.

On the other hand, you could set up a character to be pure good and then have them need to do an evil act. Something like killing someone to save a group of people (trolley problem). That would really strain the character and you could play with the philosophy of what it means to be good. By that token you could do the opposite with a pure evil character; make them do a good deed and question themself.

So that'd mean shifting from a very basic idea into a deeper one, which could be interesting for character development

The best kinds of character development come from a real challenge to their worldview.

Depends on what sort of moral philosophy you subscribe to. Some do argue for absolute morals, then there's Cultural Relativism and so on. I personally argue for the Golden Rule, so there is no distinct good and evil but rather acts humans, as an inherently selfish species, can not condone because they might be committed on oneself.