The US is reaching when they seek his extradition, and many countries in the world would outright deny the application.
And the basis of an extradition is that the crime was committed in the requesting country, even if it was done so remotely.

Making heroin in the US is illegal.
Hundreds of tons of it are made in Myanmar every year without the US demanding extradition of the producers.
Until someone tries to import that heroin into the US, because THAT’s the crime in the US.

As you point out, Assages only involvement in the crime was encouraging someone else to gather information for him - something journalists do all the time.

Whether or not we like Assange as an individual is beyond the point, there’s a definite “greater good” point to be made here.
War crimes were committed and covered up.
Without wikileaks, that may have never come to light.
Even without punishing the individuals involved, KNOWING that this information might leak out can help prevent these things happening again in future.

Journalists need to be able to publish with protection.
And Assange being personally unlikeable doesn’t change the role he was acting in, no one should get to say “he wasn’t employed by the wall street journal”, or “she doesn’t have a journalistic degree”.
Because a foundation of law in all the countries involved here is that the truth is protected, and Assange published provable facts.

And the US is trying to punish him for doing so.