There are a few major concerns:
-Iran using a nuclear weapon on Israel. The obvious counter-argument is MAD. However, that could be less successful when the two countries are closer together, IE less warning time for a nuclear strike. We also have to factor in the religious extremism of Iran. Perhaps, you could see the Iranian government overthrown by a more liberal moderate youth movement, which leads the religious leaders to a desperate point of wanting to go out in a blaze of glory and take the country with them.
-A Middle Eastern Arms Race: Iran having a nuke could inspire Saudi Arabia to develop nuclear weapons. Saudi Arabia with nuclear weapons would more more dangerous than Iran. That in addition would introduce nuclear weapons to the intense Sunni-Shia conflict with Pakistan and Saudi Arabia on one side and Iran on the other. We've seen the atrocities that ISIS has committed in the name of fighting Shia Islam, that logic could extend to using previously unthinkable weapons.
-Iran being emboldened by a nuclear deterrent to cause trouble in the region. Nuclear weapons can be a trump card in geopolitics. Iran might be able to pursue their regional power aims without inference because their neighbors are cowed by their nuclear weapons.
All that said, I'm of the opinion the more engagement with Iran is the best option. Iran is actually not our natural enemy, since they practice the minority form of Islam. We could actually see them as a ally of convenience in fighting Sunni extremists like Al Qaeda and ISIS. Just go back to the 70s, the US, Israel and Iran were allies. Israel actually worked to develop a fighter jet with Iran. That's not to say it's going to be easy or will probably work to engage, I just think it's a higher margin play than isolating them completely.
The concern I have with what you call engagement and I call appeasement is that the worst aspects of Iran are institutional. The entire government is structured to maintain rigidity, both domestic and abroad. The religious establishment in Iran want to see the government acquire a nuclear weapon in order to advance the interests of Shia Islam.
The Supreme Leader, the country's actual leader, is not held accountable by the public. The President is theoretically held accountable, but that isn't the case in reality.
"Engaging" Iran means that we meet to pursue the government's interests beyond or besides nuclear weapons. They give up on nukes, we work together on economic development or disease eradication. The regime's interests, however, all lead to nuclear weapons. The only chance engagement has is if the West were to radically shift their foreign policy in order to tip the scales of regional power in favor of Iran over Saudi Arabia. As you said, they want a nuclear weapon, in part, to strengthen their diplomatic hand when they get caught causing trouble. The only thing that could equal the weight of a nuclear weapon at the negotiating table is a strong security guarantee from the United States and its allies.
I don't think anyone would even remotely considering providing a strong security guarantee to Iran and being on the hook when Iran's regional powerplays go bust. That leaves Iran with one option to become the predominant regional power: a nuclear weapon.
Well, here's the thing, engagement might not work. But, there isn't an easy answer. The military option has its own massive downsides and it's not a 100% guarantee that Iran will be unable to pursue nuclear weapons in the future.
But, by engaging you can get inspections of their nuclear sites. You can build mutual trust and you can in the long-term empower reformers. Because, the more the US is this boogey man that they can use to whip up nationalism, the more the religious nuts can control public opinion.
And, you can always back away from a deal if Iran doesn't follow our terms. It's not just a matter of trusting them forever into the future.
It's easy to criticize these foreign policy decisions, but that's because some of these problems are difficult to solve. And, for all the Neville Chamberlain talk, there are plenty of examples of diplomatic engagement working.
