The premise of your question isn't quite right - the wall was never completely torn down and won't be, because certain sections were deliberately left standing as memorials. That was actually a conscious decision made after 1989, not because the government forgot about it or was too lazy.
After the wall fell, preservationists and historians quickly realized it made sense to preserve some segments - simply to make history tangible. The East Side Gallery is the most prominent example, but there are other pieces around the city too. They didn't want to pretend that era never happened; instead, they wanted to create a visual memory of it. Most of the other sections were torn down pretty quickly, but these historical stretches remain intentionally in place.
It's less about delays than about deliberate choice - similar to how ruins or old city walls are preserved all over the world. The Berlin Wall is an important part of German history, and precisely for that reason it makes sense that not everything disappeared.