I believe the conversation was necessary to understand Archer.
Without it you wouldn't even begin to see what Shirou awaits if he decides to follow "his" ideals.
UBW Archer is, so to say, Kiritsugu incarnated ... and the viewers, who watched Fate/Zero right before this, know what happened to him and what he felt when he came to realize what he has done.
I still have problems to decide who is in the right between the two.
It's also worth noting that Archer never says anything about having to fight his own self in the past.. as if it's the first clash between the two in the "loop"
What happened to Archer(Future Shiroe) during this/his Grail War? Won't Shiroe's (present Shiroe) life and fate change, after all, he "met" his regrets and might be able to change/overcome what will happen because of that.
I'm not sure if I'm reading too much into it ,but to me, after what happened in Fate/Zero:
Fate/Stay Night: Fate is the first loop, and Fate/Stay Night:UBW the second. (that's totally not a fact)
UBW-Archer knows alot more about Saber than Shiroe himself - Fate Shiroe had a very close relationship with Fate-Saber
Fate-Archer never really confronted Fate-Shiroe, he disliked him (alot) but not even slightly as much as in UBW.
Thus, Fate-Shiroe - and by that Future-UBW-Archer (this is getting complex) - realizes he has to stop himself after what happened to him. (after he turned into a guardian himself etc.)
and UBW is the loop where Shiroe has a chance to escape his fate(for example) by knowing what will happen and having Rin by his side... and if that's not possible, at least he can look at himself and have no regrets, because he *decided* to do it this way, fully knowing the consequences.