Shaykh Mansour Leghaei has responded to a similar question as follows:

"The time of the caliphate of Imam Ali (as) was one of the hardest periods in the history of early Islam. For the first time in history, three civil wars were imposed on Imam Ali (as).  During the periods of the previous Caliphs several innovations had occurred and were practiced for over two decades, among which was ‘Taraweeh’.  Imam Ali (as) had to stabilise the country from all the rebels on the one hand, and correct all the innovations occurring on the other. Undoubtedly, fighting the rebels was a paramount priority.

Shaykh al-Kulayni in an authentic narration quoted a long narration in which Imam Ali (as) listed numbers of innovations and how much he tried to stop Muslims from practicing them. As for ‘Taraweeh’ the holy Imam says:

“By Allah! I ruled that people should not offer any prayers in congregation other than obligatory ones. I informed them that offering the recommended prayers in congregation is an innovation. Then some of my soldiers who were fighting for me cried: ‘O Muslims! The tradition of Umar is getting changed as he (i.e. Ali) forbids us to offer the recommended prayers in groups.’ I was therefore concerned that part of my army revolt against me.” (al-Kaafi, vol. 8 p.63)

There is no authentic narration that Imam Ali (as) ever appointed anyone to lead their Taraweeh, nor that he ever endorsed it. He just gave up on them temporarily for a more important matter (i.e. fighting the rebels). Nowhere in the narrations was there a sentiment of the Taraweeh ‘being more or less spiritual’. It was all about ‘following a tradition set by Umar versus the Prophetic tradition’. Similarly, there is no authentic narration that Imam Ali (as) ever asked them to choose a leader to offer Taraweeh congregationally."

See full article here - http://www.askthesheikh.com/did-imam-ali-allow-taraweeh-prayers/