So if they were trying to get Trump on criminal charges why would they use an intelligence warrant?
What am I missing here?
You assume they are planning to use the normal criminal process. A huge amount of warrantless surveillance goes on. These people "break the law" as a matter of routine. The law means nothing to them, it is all about infomraiton and leverage, not legal process. They are above legal process. The intellignece services snoop across country lines, no warrant needed for that. It is wholesale/blanket surveillance, limited only by technology and money.
Think of it this way. It is supposedly unconstitutional for the US to tap your phone line. Okay., So the US authorities bring in somebody from the UK to do the dirty work. Legal problem solved. Information still gathered. And we do the same for them, against their people.
I think the "insurance policy" was the FISA warrant. Strxok knew the FBI had been conducting illegal surveillance. A FISA warrant provides a legal defense.