Yes, it should and they keep the terminal building as museum and exhibition location, but the airport gets closed because of very dubious reasons. Main force behind it was the socialist party, which had a very emotional campaign against an airport for rich people (but in reality pressed to have a victory of the former eastern Berlin airport of Schönefeld over Tegel and Tempelhof.). Nice fact on the politics: While it was argued that it reduces the noise over the city, most signatures against closing the airport came from people living in Tempelhof. Also, the future use of the airport area is still unknown. The current plan is to create living quarters (for mostly rich people) at the rim of it and create a huge park in the inside (ignoring the fact that a few km away, the Tiergarten district has already a very huge and expensive park area)
Most experts and pilots argued against closing the airport, not only because it was the first metropolitan airport in history, but also because it was still pretty economic for an airport, had good predictions in the future development of air travel and offered good access to the city. Well, it will not get reversed, but for me personally, it is one reason more to not vote the former SED (now called the left party). This party has only one single person, which is worth electing - the rest would be better kept in a closed psychological station...
