The problem with the international tournaments is that these players don't know each other that well so there is often not the chemistry seen when you watch league games.
Soccer is a pure capitalist sport. Very rarely will a team that isn't super wealthy win any important trophies. The goal is to effectively build up your team by winning these lower level championships, sell the players and try to climb up the ladder. Sometimes, a Russian billionaire will come along with some extra cash in his back pocket to buy a team and make them a top contender.
That being said, winning your domestic league is prestigious but winning the European cup (champions league) is where the big prize money/prestige is.