Yeah, and even with that only about 60% of the world's sea trade goes in containers because lots of things are not suitable for containerization and many destinations do not accept container ships. The fact that we can ship everything to Amsterdam and put it on trains and trucks from there means that we can really go hogwild on containerization because a few large ports can handle the vast majority of trade. It's not clear that a high port has that equivalency. A downport obviously would, but downports don't handle big ships.
Containers don't, btw, just get dumped and they don't belong to person whose cargo is inside. The container belongs to the transport company (who is often, but not always, the same entity that owns the ships) and gets used for other shipping because there's that much volume going through that port that this is reasonable. For example, when I order things from the mainland USA, they are shipped by truck to Long Beach, where they are containerized and loaded onto one of the ships belonging to the companies that ship between CA and HI. Once here, it's unloaded into that company's container yard and then then the container is driven to my receiving facility, where it is emptied out. The container then goes back to shipping company and they use it to export stuff.
It's not at all clear that these D and E ports are getting enough shipping to actually make companies keep someone on site to run a container yard. D ports are not much to look at. Some of them can barely handle a fat trader, though most are a bit more capable than that. Nor is it clear that futuretech containers are so cheap that they are considered disposable. It's also not clear that any free traders would be connected to a shipping company in that fashion.
As far as specialty containers for live goods, maybe they are low berth containers in the future. But we have cattle car containers today for shipping livestock overseas, so I expect that we'll be doing the same in the future unless the cattle freezers are cheaper and more reliable. Which may or may not be true. But I'll bet no wagyu cows or their beef are getting frosted.
Anyway, as I said pages ago, there is so little information on how trade works 3500 years in the future that you can literally decide anything you like and it would be potentially workable. If you think that there's so much gravitic tech that we basically have TK to move containers in and out of free traders, go for it! If you think the Type D starports should have cranes, container yards, and all sorts of other infrastructure, nothing says they don't and you can ignore what it says anyway.
There's no right answer. We know zilch about the economics or the logistics. I am just saying what I think makes the most sense to me, based on my understanding of what D & E starports are like, how real world shipping works (which may turn out to be an utterly incorrect model for space), and what the deckplans of the starships look like. I do not think the PC scale freighters (free/far/fat traders) are container ships in a commercial sense. They aren't laid out right, they don't fit the commercial ecosystem of container shipping, and they don't primarily operate in large ports. One of their key advantages is that they are streamlined and small enough that they can land whereever the heck they need to.
Do I normally spend much time on whatever stevedoring is involved in landing in some backwater? Not unless it's part of an adventure. But I do think that those ships are breakbulk: so pallets, crates, drums, bales, bundles, boxes, and other non-standardized size stuff. YMMV.