Three-field systems came into existence in Europe around the turn of the millennium, and coincided with the widespread use of horse collars and heavy plows. Its understandable, then, that it took some time for that system of agriculture to be developed. And, its also understandable that it would take awhile to spread.
However, what intrigues me is that four-field systems seem to date from the 16th century. Why so much later? All the crops were old world crops, and it seems to me that it would be just as much of a jump for someone to try switching to four fields as three. What was the stumbling block there, the missing piece?