It would also antagonize a lot of countries and almost mechanically create domestic pressure for foreign leaders to take a stand against the US. There is literally no better way to make non-alignment a popular political stance. Not only that, but the second gulf war has already harmed the credibility of the international order that the US and its allies have worked hard to instaurate. The US did not ratify the ICC, ignores UN war laws, operates an alternative detention facility to escape its own domestic civil rights protections, performs extrajudicial killings all around the ME and now take down political opponents abroad. That could very well be the straw that breaks the camel's back. And if it isn't, what comes next should. Not taking a moral stance on either of the things mentioned above, just observing that the increasing dissonance between official US narrative on foreign policy, and its real-world applications can only harm its prestige and credibility.
I can't think of a more terrible move for the USG than murdering Snowden.
tl;dr: The harm has been done already, killing him would only make things worse.
I'm sure it can get even weirder.
https://en.wikipedia.org/wiki/Poisoning_of_Alexander_Litvine...
Putin might be mad, but they wouldn't give 2 fucks about Snowden, if Russia got anything in return for granting him asylum they already got it.
That said the US would more likely want to exfiltrate him for this specific reason, they would want to know if and what did Snowden handed over to Russian intelligence.