The existing combination of 12V fuse panel and 120V circuit breakers in the same box is a convenience, not a requirement.
Think of the 12V system as being its own thing. It's completely reasonable to just use an automotive fuse block as your 12V power distribution point. They're readily available for people wiring street rods and the like. For that matter, Camping World had a nice one hanging on an end cap when I was there last week.
If you don't have any 120V sockets or appliances, the only 120V load in your trailer is the converter, which charges and can substitute for your battery as the current source for the 12V system.
Most newer trailers have actual 120V wiring to allow running 120V appliances from sockets, allow running the three-way fridge
on 120V, possibly an air conditioner, etc. You can choose to set up your trailer this way or not depending on your use case. As a matter of practicality, it's often nice to be able to run 120V tools off a plug in the trailer when doing work there.
A converter bridges the 120V system and the 12V system, and also substitutes for the battery in the 12V system when it's plugged in. There's usually a battery charging function built into the converter as well. The difference between a converter and a battery charger is that the converter has a switch (relay) in it that switches the 12V loads to the converter when it is plugged in, and switches them back to the battery when it is unplugged - the idea is to keep the battery unloaded and topped up when the converter is plugged in so that it's ready to work when 120V power is not available.
If you have an older parallax converter, it's a common modification to swap out just the lower unit when it dies with something newer and leave the nice metal breaker box and fuse panel in place as the electrical