The standard of living (but not personal freedoms) is relatively high in Iran. As much as the leaders of Iran need to respond to such blatant provocations by the USA, they have a lot to lose.
Iran can cause trouble in the region with their militias and proxies but if it came down to conventional warfare with the USA, they would be in trouble.
Iran has a population of 80 million i.e a lot bigger than Syria, Iraq, Afghanistan, Libya etc. It is in no ones interest for another basket case failed state in the Middle East and I'm sure Europe is fretting over this big time.
Lastly, martyrdom (dying for a greater cause) is a concept held with an especially high regard in Iran and in Shia communities. Iran has a very strong ethnic identity and they are very passionate and proud of their background as they are effectively descendants of the great race of the Ancient Persians. Given these two cultural traits, I suspect that there would be no shortage of young Iranian men willing to sign up to fight for their country.
I hope that both sides are able to restrain themselves from escalating things further.