Writing preferences change over time.
Until 1940, the expression does not seem to have been preferred by writers.
Towards the end of the century, that is why was predominantly the phrase to use.
In the 1950s, there was a trend reversal so that about 1982, that's why seems to have started gaining wider acceptance and usage.
We may have to infer that today, writers prefer the contraction over the longer idiomatic phrase.
Drawing inferences from Google nGrams is fraught with pitfalls and one needs to be cautious. They can help in supporting a broader research.
One possibility would be as StoneyB points out 'a relative increase in the number of “semi-formal” publications.' However, see also Barry England's citation on the interactive quality and how contractions facilitate reading (by avoiding distraction, or aiding in better focus.)