So I have a copy of Where Hell Freezes Over – the book they reference in the Wikipedia article. There’s a few things worth noting in that book that sheds some light on your question.

First, remember that the ice flows were constantly changing and they didn’t even have, like, an accurate map of the continent’s perimeter. So Western Group was tasked with sort of, scoping out the unknown coast (p. 14). The Eastern Group then took Western Group’s work and actually mapped out the entire coastline of the continent with low-flying surveying missions snapping hundreds of stereoscopic photographs an hour (p. 19). This all had to happen before the Central Group arrived to actually set up the base (p. 13).

That’s the other thing – not all the ships sailed together. It’s not like there was a caravan of 13 ships. They arrived and departed at different times over that period. But at the same time, they didn’t go alone… if you’re sending an aircraft carrier somewhere you have to send an escort so that no one just drops a bomb on your sweet aircraft carrier. That’s a couple destroyers, a submarine, frigates, a supply ship, all sorts of stuff.

We call that a Carrier Strike Group now – that’s 7500 people alone these days. It was a lot less back then, but building a base in the polar regions would necessitate specialized ice breaking ships and multiple supply ships. When you remember that they’re coming from like three different commands and all need escorts, it’d be pretty easy to get to 13 ships.

Also, remember a base in this case isn’t like a cabin – they needed something that could support the comings and goings of DC-3s. That’s a half mile runway. Yes, the goal was to establish the base, but they needed the base to do all the things they really wanted to do.

Admiral Byrd believed that securing the polar regions was essential to the defense of the United States (see Wikipedia). If you think about Great Circles navigation, that makes sense – especially when you think about the Arctic. But you can’t establish a base there, so where are you going to train your troops for arctic actions? Where are you going to test polar effects on navigation? That’s what they mean by training, not like, set up a place where soldiers go through bootcamp.

Hope that helps!