Wouldn’t it be more correct to say that most Americans also use a messaging app (iMessage). The rest are just stuck with SMS to have compatibility with the iPhone users.
As the iPhone was (is?) not as popular in the Europe as it was (is) in the States that might also be one of the reasons why people here ditched SMS so fast once smartphones got popular.
But it’s not “most”, it’s more like half of Americans use iMessage (that’s not an app, it’s a service, the app is called Messages), and the other half uses SMS with different apps.
The factor that moved people away from SMS in the EU was telecom companies charging for it. SMS is virtually free for telecom companies, but European companies got greedy, and people moved to WhatsApp. They tried to block it, but accepted defeat after a while.
In the US, SMS is free with your phone plan, and it became popular with young people until iMessage appeared. Since iPhones are still subsidized by US telcos (afaik, correct me if I’m wrong), a lot of young people have iPhones and use iMessage, that’s far superior to SMS.