Maybe I was a bit young to have a solid perspective on this, but I too remember JT being a huge hit from the get-go. In fact, since the Rolling Stone review was mentioned, I actually remember that review being one of the main reasons I went out and bought it right away--I specifically recall the reviewer predicting that this would be The Big One for U2, whom I already liked anyway; I think there was maybe some mild criticism to the effect that some of the lyrics were a bit cliched but, you know, that's true lol. I remember that year as clearly being the moment when U2 made the leap from mostly being college radio darlings (though most people knew 'Pride') to being one of the 'biggest bands in the world.' It's true that JT didn't sound much like earlier U2 nor like any particular other album that was big at the time, but I don't have any memory that it was widely seen as a 'challenging' listen, or not very accessible or whatever. WOWY and ISHFWILF pretty much went straight to #1, didn't they?
My memories aren't detailed enough for a sense of precisely how big 'Streets' seemed compared to WOWY and ISHFWILF, but it definitely featured prominently in the JT tour, you can see that much in the Rattle & Hum film. For sure it got heavy radio airplay upon release, and was far better known than 'In God's Country' which I think was the only JT single that never went much of anywhere (in the US at least).