I've just checked: there are plenty of direct flights each day from Berlin to New York for example. It is not the central hub like Frankfurt is, but I doubt you won't fly to Berlin because it does not have enough infrastructure...

There might be transatlantic flights from Tegel, I'm not sure, but they're rare. Moscow and the Canary Islands are more or less the limits. I usually find myself going through Frankfurt, Paris or Amsterdam for intercontinental travel.

The lack of direct flights is partly due to the short connection to Frankfurt from where you can connect to most destinations in the world. That's also why some other German cities (Hamburg, Cologne, Hannover) have few transcontinental flights, despite the demand. There has been an increase in direct flights from Berlin recently but towards the US, Heathrow and Frankfurt are on the way and BA/LH can price out competitors easily.

Berlin is certainly underserved given its size but that's just the Frankfurt effect (an airport with >60m passengers p.a. for a city <1m population).