Why would the present shape of the continents not fit perfectly into the shape of Pangaea and what things might have changed the continents' shapes?

They would fit roughly together but not perfectly due to years and years of erosion.

As evident as Africa and So. America are that they were once joined.

Erosion does not work.

Even with that they will not fit. Try it with cut outs.

But shrink the size of the earths sphere to about 1/2 its size today and they fit perfect.