That converter article is pretty much out of date. Most converters now can supply over 50 amps, and the voltage regulation (how stable the output voltage is) is very good.
Think of the converter as another battery whose voltage is much more constant than a lead-acid battery. It works in parallel to the house battery. When it gets to its maximum current, it will usually overheat and pop a thermal breaker. It's not as efficient as a lead-acid battery, though, which is why it has a fan, which you will hear running depending on the current draw.
Often, the reason why the converter alone will not run the landing legs is because there are a lot of current draws (standard 12 volt bulbs draw close to an amp or more, a good reason to go to a lower wattage bulb or LEDs), and they can add up quickly. When you add the big load of the landing legs, it can reach its capacity very quickly.
A charged battery can supply a lot of current in parallel to the converter for those big loads, and it charges at a much lower current over a longer period of time. This reduces the overall load on the converter. It's kind of a hidden load, though. If you are on battery overnight when it's cold enough to run the furnace, the next morning when you first start the generator, a good portion of its power is going to recharging the batteries, and you may get a surprise when you turn on the microwave to heat up your coffee.
Bob
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