When traveling via Mass relay, it shows the route you're going to take and which systems it passes through.
Does passing through extra systems on the way to your final destination have any in-game effect, or is this essentially just for flavor?
From what I could tell, it never made a difference for travelling. The multi-stage trips seem to simply be to keep the series' canon. From the mass effect wiki:
There are two kinds of mass relay, primary and secondary. Primary relays can propel a ship thousands of light years but only link to one other relay, its "partner"
As such, it seems that each relay can only be linked to exactly one other relay (though some locations may have multiple relays). Travel between two non-linked locations rely on heading through multiple mass relays.