There are three possible, and to some extent interlinked, scenarios under which Pakistan could become motivated to dramatically reduce or altogether cut support for the Taliban and the Haqqani networks, and perhaps even start targeting their networks in Pakistan:
Pakistan-India relations significantly improve;
The military-intelligence apparatus loses its predominant power in the Pakistani government and becomes subordinated to an enlightened, capable, and accountable civilian leadership. That means that both the Pakistani military and the country’s civilian politicians would have to undergo a radical transformation; and
Pakistan develops the political and physical resources, and wherewithal, to tackle its own internally-oriented and metastasizing terrorist groups, such as various Punjab Taliban groups: Laskhar-e-Jhangvi, Sipah-e-Sahaba, and the Islamic State in Pakistan. If those threats become mitigated, Pakistan may have more stomach to go after the Afghan Taliban and the Haqqanis.
In this video from 30SEP Aziz is saying that his mission is to eradicate Christians, Hindus, Sikhs, Jews, Qadianis (= Ahmadis) and Shias. https://twitter.com/UNewsTv/status/1443461135404052481
The problem for Pakistan is that ISI might loose control of their assets. In 2007 this happened at the Red Mosque https://en.wikipedia.org/wiki/Siege_of_Lal_Masjid