Even without nuclear warheads, Iran possesses an incredible number of rocket and missile platforms that as with all modern military forces provide coverage from short to long ranges and in multiple types for engaging land, sea and airborne targets. These rocket and missile systems are the qesheth that Jeremiah speaks of. There is no reason given for the breaking of these weapons systems, it's just that the Lord of hosts has declared it will happen.
As in ancient times when Persian/Median armies launched massive barrages of arrows at their enemies, so too the Iranian military of today relies very heavily on their modern day equivalent. Iranian warfighting doctrine dictates mass barrage-style launches. Iran can be seen exercising this capability every couple of months or so, and in some instances photoshopping the images to convey ridiculous numbers of rockets being launched.
In any event, the consuming of this important region of modern-day Iran by the ravages of war would create far reaching effects, not the least of which would be the downgrading of Iranian military capability and the loss of Iran's primary industrial and oil and natural gas producing sector, the overwhelming majority of which lie within the heart of ancient Elam.
Addendum: To those who would erroneously interpret that Jeremiah's prophecy was fulfilled thousands of years ago, I would recommend that they seriously reconsider some key points before blurting out their ignorance on this topic.
1. Jeremiah lived and prophesied during a critical period of Judah's history. As noted above in Jeremiah 49:34 this prophecy was given in the beginning of the reign of Judah's king Zedekiah. Zedekiah's reign began in 597 BC. No earthly events of the type and in the place prophesied by Jeremiah have ever occurred since 597 BC and forward to the present. Therefore, and without question, Jeremiah 49:34-39 constitutes an unfulfilled prophecy regarding the modern, latter-days country of Iran.
2. In Isaiah's own latter-days prophecy (see: Isaiah 11:11-12) which mirrors the prophecy of Ezekiel 37 concerning the re-assembling of "the outcasts of Israel" gathered together with the "dispersed of Judah," the prophet Isaiah names several nations from which the Jewish people of the Roman exile of circa 66-73 AD would return to the land of Israel:
From Pathros and Cush,
From Elam and Shinar,
From Hamath and the islands of the sea"
Clearly, the use of Elam and the other national names of antiquity for latter days prophetic fulfillments is a common theme for many of the inspired prophets of God, and should not constitute a problem in any exegesis, including this one.