Bethlehem is five miles south of Jerusalem. The direct route for Persian visitors would be to pass through Jerusalem. It was perfectly natural that they should call upon Herod - not to mention politically advisable.
Sorry, this is a total miss.
Herod was a self aggrandizing psychopath and a murderous despot. Even people who couldn't read the stars knew it. I can't recall the details but in Mass on Sunday we heard a small litany of the friends, wives, relatives and rivals he had killed.
Therefore, to "call upon" him, alerting him that a rival king -- THE rival king -- had been born, is about as advisable as doing jumping jacks with flask of nitroglycerin strapped to your belt.
Futhermore, why avoid him on the way back if it was "advisable" to "call upon him" on the way there?