No other league has needed to try. All the other sports were already international. That’s why the NFL is trying to swim up this stream. They don’t have an Olympics spawning the game in other countries, they don’t have a FIFA (badly) overseeing the sport globally, they don’t have any kind of international competition inspiring the next generation of players. Heck even NASCAR can pull talent from around the globe because everybody races something. It might be an impossible task, but it’s a mountain they need to climb.
Attracting talent is a whole different story. The NFL doesn’t need to put any teams in Europe to attract talent — because the NFL doesn’t groom their own talent anyway. The NFL already has a great avenue for getting talent from around the world, and it doesn’t cost them a dime. College teams have been recruiting foreign players in droves, and they are now showing up all over the NFL. I think it was the 2013 draft where 5 foreign-born players were drafted in the first round alone.