Why didn't Emperor Taizong of Li Shimin make Li Ke a prince?

At the end of the day, Emperor Taizong wanted to establish Li Ke because other older princes were either demoted or killed for taking the throne, or they were really helpless. Although Li Ke was once demoted twice for stepping on crops and gambling, there was nothing Emperor Taizong could do except Li Ke. However, it is obvious that Emperor Taizong's idea of establishing Li Ke was not well thought out, but on a whim. Because if Emperor Taizong really wanted to change Li Ke, or was determined to change the storage, then Sun Chang Wuji would never have a chance to "fight in the dark", let alone make a final decision just by a word from his family. After all, the world belongs to Li, not his grandson. In the seventeenth year of Zhenguan, although Sun Chang Wuji was an excellent Si Tuleideng, Si Tuleideng's position was only a hollow position as far as the regime of the Tang Dynasty was concerned. With no real power at all, how can Sun Chang Wuji keep state affairs? At this time, he was dead, but these ministers of Fang, Li Jing, were still alive, and Emperor Taizong was in the prime of mastering the military power. How can you let Sun Chang, who has neither real power nor military power, control state affairs indefinitely?