The New York investigation stinks, but then I'm going off of memory, as I recall the State AG had previously made clear his intention to run Trump through a wringer, and not just Trump, but everyone associated with him. His basis for doing so basically boiled down to "He won an election I don't think he should have."
Presidential immunity is a side-issue in this case involving the State of NY, private citizen protections against abuse of investigative authority for purely political objectives is (un-ironically) on the agenda here.
The NY Case is almost entirely political in nature, and only exists because Trump is PotUS. Thus making it a prime candidate for a case which should wait until Trump(and the AG) are both out of office.