What immunity doesn't address is the individual's first amendment right to freedom of speech. Freedom of speech must include the freedom to remain silent. Nothing in the constitution gives the government the power to compel expression.
Fourth amendment protections against search and seizure should apply as well. The government is trying to force these people to provide the contents of their minds. Again, there is no constitutional justification for this.
The constitution sets out strict limits on government power. This use of the grand jury system is a clear violation of those limits and a moral outrage.