What part did the machines play in the demise of Smith at the end of Matrix Revolutions? Smith's defeat was due to lack of purpose since Neo was dead, but if that is the case then why did the machines "zap" Neo and destroy him and thereby Smith, if Smith was already facing deletion due to having no purpose?
Smith's defeat was due to lack of purpose since Neo was dead ... why did the machines "zap" Neo
I won't call it an unfair reading, but I don't think this can be taken as a given.
I don't have the energy for a well-cited answer this late, but my interpretation is that Smith, who has ~infected everyone in the Matrix, ends up helping Neo fulfill the function/purpose of The One (by disseminating the code Neo carries).
We don't know exactly what fate awaited Neo behind the other door at the end of Reloaded, but I think the dissemination of Neo's code was always going to kill him.
For what it's worth (this isn't quite how it appeared on screen and I'll snip some bits out since it's several pages) here's this section in the script:
... [in medias res, scene 764] ... Smith is about to press his frenzied assault, but he freezes, the image of Neo laying splayed, suddenly familiar. SMITH (CONT'D) Wait... I've seen this... This is it! This is the end! ... SMITH (CONT'D) Yes, you were laying right there, just like that... And I... ... SMITH (CONT'D) I stand here, right here and I'm supposed to say something... I say... ... SMITH (CONT'D) Everything that has a beginning, has an end. The familiar words suddenly clear Neo's mind. He looks up as Smith looks down. SMITH (CONT'D) Don't be afraid, Neo Neo almost can't believe what he just heard as-- ... SMITH (CONT'D) What? What did I just say? In his confusion, he looks to Neo who now understands. SMITH (CONT'D) No, No. This isn't right. This can't be right! One final time, Neo rises to his feet. SMITH (CONT'D) Get away from me! NEO What are you afraid of? SMITH It's a trick! NEO No, it's what you want. It's why you're here. SMITH No! NEO You were right, Smith. You were always right. ... NEO (CONT'D) It was inevitable. Smith's eyes fire, a scream rises up from him and in a crackling, blinding flash of lightning-- He stabs his fist into Neo, who stands with his arms open, accepting the blow. ... 765 INT. MACHINE CITY TOWER - NIGHT Neo's body hangs motionless, supported by the passage as we see as Neo would, an empty husk that is being filled, liquid light pouring into him from every connection. ... [... near the end of 768 EXT. MATRIX CITY STREET - NIGHT] The old Smith, at the center of the crater, fights to the last. His scream rails against the buildings as he bursts open and is consumed by light. From high above we see the explosion of blinding light sweep through the entire city as-- 769 INT. MACHINE CITY TOWER - NIGHT A final surge rushes through Neo, his body convulsing against his metal coils and we see the light drain out of him and his body falls quiet and still. Neo dies.
Many of the details this question hinges on are ambiguous here, but it's clear that Neo isn't dead until the same time or after Smith is.