Interesting. Another point for Hawkeye as ISFP, as he almost died to save a single child. Black widow would have radioed one of the more durable Avengers to go get the child.
Yeah, exactly. That would have been a "rational" response... at least if there was time to send someone else. Hawkeye AND the child getting killed
seem like negative modifiers, to be balanced in an equation -- but for someone who is just empathetic and also just says, "The kid's in trouble and needs me even if we'll both get hosed," it seemed like the most obvious choice to run out there. He didn't even really think much about it, he just did it from the gut.
I just rewatched the Wrath of Khan, and while Spock has a similar situation he's processing, he also had no real family he was leaving behind and you can actually almost see him "calculating the pro's and con's" and deciding that the best odds of success for everyone were for him to go in that radiation chamber, regardless of his rank or other relationships; he ends up making a very rational decision based on the maximized positive balanced sum of his calculation. The emotional fallout afterwards is secondary.
As for the "seemed really stupid", I'm sure Nick Fury would agree with you, which is why he brought the helicarrier to run rescue operations, so the Avengers could take care of the task at hand.
Yeah. And I admit, I'm more "balance sum" and just saw it as, "if that thing goes down, all of humanity is dead; so make sure you don't flub that, the rest is secondary."
Though, I did think the most powerful bit of the movie was Scarlet Witch's reaction to Quicksilver being killed...
That was good. And acceptable based on her personality... but of course created a bit of a problem in the meanwhile.

But she was serving her own values there for good or bad; it made sense.