Their job is to enforce immigration laws inside the U.S. When illegal immigrants are travelling domestically, it involves ICE.
The crime starts when the border is crossed, it doesn't end once you are illegally in the country and travelling domestically.
One can use this logic to create an omnibus surveillance apparatus covering all aspects of communications, commerce, etc.
We do not give other law enforcement similar deference, even though it might help them in some fraction of cases. For example: SEC could prosecute more insider trading if it was able to wiretap all domestic communications.