East Germany suffered a lot of emigration due to economic sanctions (they couldn’t trade with most of the world due to west germany’s lobbying and many of the people leaving where formerly expelled people from east and central Europe and therefore had no roots in the east, where housing was very much in shortage.)

So if everyone who wanted to leave got shot, then there would be millions of dead germans recorded. Of course crossing a militarized border as a propaganda act to receive a more cushy life in the west (West Germany exalted defectors like South Korea today) would result in oneself getting shot.