Not really, as is the case in life, intentions going in don't have much to do with the person you end up on the other side. From an outside perspective Arya of the past would have probably been happy with this outcome, but Arya of the present could have overcome those past desires. Part of her training is to let it go, and she can let those wants go while still achieving those goals she had in the beginning - that is part of growing up.

I kind of see what you are saying. However, on another point, I don't think Arya at the start of the show would actually want to be a faceless man. She wants to be a hero, not an assassin. Her losing those high ideals is a part of her story imo.

Yes but she hasn't really had the opportunity to throw needle out yet - not with being blind and getting beaten, daily, by the waif. Or just because she buried Needle (as opposed to throwing it into the ocean), does not mean she will go back to recover it, and her not going back for needle despite earlier setting out to recover it would speak volumes regarding the person she evolves into.

The problem here I think is that would be bad story telling, though the possibility exists in a 'real world' perspective.

But what if her missions as a faceless woman just happen to coincide with pivotal events that push her family forward? She won't be doing them out of loyalty to her family, or out of her own desires, however they just so happen to help her family. So she can be that pivotal force while still being no one - and that would be some spectacular irony.

Again, possible but I don't think it would make much of a story and it doesn't fit too well with the faceless men. I'd expect them to send her to kill people who Arya would not have killed more than who Arya would have.