Shas does not own the Sephardi - Mizrachi Israeli representation. It's been decades that Israeli voters of all Middle Eastern backgrounds have voted for right, centre and left parties. It's known in the past since PM Menachem Begin's administration, that great numbers of Sephardim/Mizrachi usually have voted right. However, the current generation has possibly changed their voting patterns to more moderate parties. It's nothing really to do with PM Netanyahu's choice amongst Likud members but more with coalition representation of the pluralistic electorate in Israel. It's questionable whether even with such a new coalition there would be significant changes to Israel's foreign policy and domestic policies especially with regards to living conditions in Israel. That's tampering with shifting ideological approaches of the past to move forward...like dancing the Tango!
Jerusalem light rail conductors striking over new train schedule (Haaretz)
from the article: Likud officials threaten 'intifada' over Netanyahu's coalition plans