What did Conte do for Italy? He didn't do shit for Italy's national team.
He didn't, yes, but he's no exception to the rule. Top league managers are more than often bad national team coaches. Both come from different worlds. Instead of coaching their team on a daily routine, a team which they assembled to their likings from a broad international pool of players, national team managers have to live with a very limited amount of time to convey their ideas to players they'd hardly choose, if they had a choice.
This is a two-edged sword and I don't think that Löw would be a good manager for, let's say München, since his name came up. Managers that actually were both successful in a league and a national team are scarce and this disparity has become bigger in times of such complex differentiations we face now in league football. There's also another hurdle I've been thinking about lately: priorities.
In order to succeed with a national team, you have to become what we call in Germany a Fußballnation, a football nation. That means building structures, that means providing means and accompany players from their youngest age. That also means to sacrifice. The British are not ready to sacrifice their Premier League for a World or Europa Cup. The old continent sets different priorities. That's why in other countries, one team dominates a league, which is not the case in Britain.
Consequently, this team is made out of 80%, what we will see in the national team, which will consist of players, who know each other. A
real team, so to speak. A manager has then only to provide a good atmosphere and protect the the health and self-confidence of his players. That's why Podolski was in Brazil, that's why dehydration was such a big issue there for Löw. Anyway, it's a tl;dr story, but one that preoccupies me lately.