I'm no historian—

I'd just add a slight agreement to selection bias. Handwriting wasn't necessarily better at the time. I only have two counterexamples on hand but you could easily find more; here and here is a piece with no better handwriting than the average person would have today. They're written by George Washington.

A lot of documents were important enough to have a professional calligrapher recreate them; things like the Olive Branch Petition, Declaration of Independence, U.S. Constitution come first to my mind from the colonial era.

It's worth noting that the most used instrument for both handwriting and calligraphic writing in this time period was the quill, a rather cumbersome instrument. It made ordinary handwriting a little more difficult (and much less neat) and might have made calligraphy somewhat more difficult. The dip pen was an amazing creation that came to public use in the second half of the 19th century if I remember correctly.

From a calligraphy perspective, the script that you see all these documents set in, and executed with a quill pen, is usually called English Roundhand and is defined by uniformly thick downstrokes. Roundhand was usually used as a form of handwriting and not calligraphy, you could say that the script in the constitution is more of a really pretty Roundhand. Roundhand is the precursor to the very refined and ornate dip pen forms of Engrosser's Script and Copperplate (which is itself a precursor to 'Modern Calligraphy')