I think you misunderstood me, Russia _was_ on a path towards NATO in 90s to mid-2000s. There was cooperation, joint exercises, etc.

E.g. from a conversation between Clinton and Putin in 2000:

> Clinton: I am serious about being ready to discuss NATO membership with Russia. I recognize that domestic considerations inside Russia will prevent this for now, but over time Russia should be a part of every organization that holds the civilized world together.

> Putin: But I'll let you know that when I was asked about possible membership for Russia in NATO, I supported the idea.

Regarding "reason to exist", there's always a concern about Middle-East, China, etc.

Funny enough that you remember it was as "Russia applied but was rejected" but from this talk it's clear Putin is much less interested in Russia joining NATO than Clinton.

You can find full text here: https://nsarchive.gwu.edu/document/33393-document-3-memorand...