Opening Port is not something I am crazy about, but it does make sense in 4er and even 3er. It is far too easy with multiple players to end up with 0 or 2 villages and get locked out of contention, particularly if you are also fighting off attacks. It also makes sense to open Port if you are going be using low cost terminals and are heavy trashing. For instance, Port/Chap/Alms works really well as you never collide on Chapel on the first shuffle, you can time your shuffles better, and you can still get some fun terminals to quickly build back buying power (e.g. things like Fortune teller, Scavenger, Horse traders, etc.) quickly. Likewise if you are doing something like Steward/Port/Wt it can be worth it early on to grab Ports so you can buy terminals and not worry about buying Silvers to maintain buying power (you really do not want to be playing Steward for cards or coin just to buy Port later).
Port also plays really nice with cards that care about value. Feed your Salvager over two turns, Forge a province next turn for $4, or Tr -> Upgrade to pick up two nice $5s. And like all cards with any sort of on-gain effect, Port is a pretty nice feed for scaling TfB.
In terms of how games actually play out, Port makes engine get going a lot faster. Spending half the normal number of turns acquiring early villages is nothing to sneeze it; in some cases it may effectively give you an extra turn with each Port buy. It is particularly handy if your draw or payload cards fall in the $4 range. On the flip side, the Port pile tends to empty faster and empty fully, unlike a lot of other village piles, this makes it a good bit easier to reach end game. One or two other fast piles can very quickly turn the game into a duchy race or an instant 3-pile. None of this is huge, but Port should make you consider marginal engines a bit more and consider a bit more building with an eye towards a possible 3-pile.