Simple electoral mathematics demand it.
Labour can only have an inquiry into anti-Semitism if it scratches the surface.
The methodology being used by the Jewish Chronicle in its story about Naz Shah MP, and Guido Fawkes in a series of recent cases to break stories of extremism and racism involving prominent British Muslims, is not revolutionary. It is that Conservative Campaign Headquarters and Hope Not Hate used against UKIP candidates in the 2014 European elections and 2015 UK elections. Trawl through an individuals social media accounts, look for anything which could be considered (or actually is) racist and use it to hit the candidate, hard, via a compliant media. Some of the stories proved to be false and led to embarrassing apologies, others were not, but they got the job done.
Anti-Semitism may or may not be a deep-rooted problem within the left. It is deep-rooted however within British Islam, as Medhi Hasan observed in an important article in the New Statesman in 2013. Whilst the British left is at times determined in drawing a distinction between criticism of Zionism as a political ideology, and criticism of Jews as people, examine the posters and messages on any pro-Palestinian demonstration and you will see this distinction rapidly becomes blurred, especially among politically active British Muslims. If Labour's internal inquiry starts examining attitudes to the issue of anti-Semitism among constituency Labour parties in London, Birmingham, West Yorkshire, East Lancashire and Greater Manchester, things are going to get very messy indeed.
I don't think Jeremy Corbyn's Labour party can afford to raise that stone, because we know what is crawling underneath. The problem Shami Chakrabarti faces however, is that if she does not raise the stone others, the Jewish Chronicle and Guido Fawkes to take just two examples, will do it instead.