The reason players don't push aggressively is because the cloest target is the easiest to hit. Their ship gets focused by the many enemies of the other side and will easily get sunk early in a match if overstepping.
There was a recent Brawl that was 12v12 Battleships (if I remember correctly) that had a surprising number of complaints about battleships that wouldn't push up. The inability to push is more gated by the amount of threat on the board than a specific class or situation, though those can certainly be things to consider in their respective situations.