A wire's capability to safely carry a specified amount of current is not directly related to how the wire is sized in a particular use.
The overall capacity (or "ampacity") has to do with the amount of heat created due to the current flow, and the coating of the wire being able to safely withstand that heat. You will find that much smaller wires are rated for the currents that most of us use significantly larger wires for. The reason for this is that wires have resistance. The smaller the wire, the more resistance. Resistance in an electrical circuit (which is what you're creating any time you hook up wires and current is flowing) dissipates power and creates a "voltage drop". There is plenty of reading you can do on the subject beyond what I'm simplifying here.
The reason to oversize (or even supersize) the wire is to minimize voltage drop, and the losses and problems that come with it.
As you have correctly deduced, you can't pull 600A from a device only capable of generating 100A (though if you look at the BEMM and the alternator power curves, you'll see that the 150A can generate more than 150A. Same for the higher current models.). If it's capable of 100A and you hook something up that will draw near to the max, the alternator will do it's best to supply it. While it does so, it will heat up significantly. It simply isn't designed to operate in this range for an extended period of time without some sort of permanent damage occurring. If there's a high temperature cut-off, it will shut down to protect itself. I don't know whether this exists on the Transit, but I would think it should.
Back to your batteries, Battleborn itself says to charge at 0.5C for the best lifespan. This means charging a 100Ah battery at 50A, or 200Ah at 100A - and so forth. Unless you have a good reason to want to charge them faster, why would you risk shortening the lifespan unnecessarily? In order to do this, you will need a device that limits/controls current and keeps it to a maximum of whatever 0.5C is for your chosen battery bank. With presently available options, this narrows it down to a DC-DC (B2B) charger of some sort. Picking a specific brand is probably beyond the scope of this discussion and subject to heated debate.