I mean Rush, U2, and other bands dominate and sell out huge arena/stadiums all over the world. I think saying U2 from Fire to Pop were in fact the biggest band in the world. The Beatles were the same way. There were huge and making headlines in Japan and other places.
Most of these bands TLK has been talking about also are huge on charts outside of the European/American countries as well.
I imagine if we were (and are probably headed this way) where China/India are the dominant voices in both the economic/political realm, then we will see the same kind of crossover with their artists.
Being that bands can have that kind of stage means they are influencing things. U2 is for sure a big influence on Radiohead and Coldplay, for example. And not just musically, like
@jamieanderson1968 pointed out their circumvention of the normal route to success meant that it wasn’t just the punks who could do that and be huge opening the door for the whole indie movement of the eighties that in turn allowed the Alternative movement of the 90s to fundamentally change the very nature of pop music allowing for Hip Hop to be the juggernaut it is today.
It is indeed part of the history.