> ... the US would remove the Taliban very quickly...
No, no, no. The Taliban were broadly distributed throughout Southern Afghanistan, and they had a cross border sanctuary in Pakistan.
For its own reasons (Kashmir and the regional rivalry with India), Pakistan didn’t want to alienate the Taliban, and their military and ISI thus had extensive relations with the Taliban.
The US did not have enough leverage to get Pakistan to shut down the Taliban on its side of the border, and likewise did not want the destabilization of a nuclear state with borders on China and India that would accompany violations of Pakistani sovereignty inherent in large scale bombing.