But many of the other phases involve each player doing what they want on a particular state board before moving on to the next state board, so everyone would have four smaller turns instead of one large turn.
Which other phases are you referring to?
I haven't read the VG version of the rules, but they seem to be causing a bit of confusion. I play the 2nd Edition and each player acts once in the Meeting Marker phase (i.e. place up to 4 in each of the active boards all at once before proceeding to the next player)