The decision to hub in Frankfurt (and then later in Munich) has both historical and business reasons.
- Historical reasons
After World war 2, German airlines were not allowed to fly into Berlin, because Berlin was not officially a German city, but under control of the four powers that won the war (USA, Russia, UK, France). That prohibited Lufthansa to locate any planes there.
Also because Germany was divided until 1990, all the action was basically in the democratic and free-market western part. Frankfurt was perfectly located there, as it is right in the middle of West Germany. It also didn't hurt, that the US Armed Forces had a large airbase right next to Frankfurt Airport.
- Business Reasons
While Berlin or Hamburg are Germany's largest cities (Berlin is the largest and Hamburg the second-largest), they lack business strength, especially in their surrounding area. After re-unification, Berlin was mostly devoid of any industry, didn't have any large corporate headquarters and had pretty much no significant economic activity in 100km radius outside the city. This situation has improved over the last 28 years, but Berlin is not the economic powerhouse that Paris is for France or London is for the UK.
Hamburg was a much more vibrant city in terms of its economy, but its economy is much more maritime-based due to its large international harbor. Also, as Berlin it lacks strong economic activity in its immediate surrounding area.
So if you look at Frankfurt, do not just see Frankfurt's importance as the financial hub of Germany and Central Europe. You also need to see the economic strength of its "Hinterland", meaning the Rhine-Main-area that includes a radius of 50-100 km around the city center. That covers roughly 5.7 million people (7% of the German population). Now if you add in places like Cologne or Mannheim/Heidelberg/Ludwigshafen (home of BASF, SAP for example), that can reach the FRA airport in about 1-1.5 hours, you have a lot of economic firepower that will power traveller numbers.
Munich is similar to the Frankfurt story. The city itself is nearly twice as large as Frankfurt and is THE economic powerhouse in Germany housing corporate headquarters of firms like BMW, Allianz, Munich Re, Linde for example. Its "hinterland" is also very active economically, providing ample fodder of private and business travellers. Now add in the area of Salzburg in neighboring Austria, that is much nearer to Munich airport than to Vienna and you have your answer.