Hm, where to start with this? Older styles of writing are a whole field of study unto itself, called paleography. It's both a necessity for historians who want to read older documents, and also a tool for dating, determining authorship and other things. Hence why this subreddit has a whole list of books on paleography in its wiki.

Anyway, no, far from all documents were written in cursive. In many times and places cursive styles were not used at all. E.g. a 9th century west European document ought to be in minuscule script. Cursive didn't exist then.

The reason why cursive was invented, and was and is used is precisely because it is more practical, in that it is faster to write. It's the exact opposite of what you think - People used cursive more , and more difficult-to-read cursive, in private contexts like letter-writing, because speed had a higher priority than legibility, unlike in a formal document where legibility and fewer mistakes were more important than finishing it quickly. There's also no single style of cursive, there are many of them, again depending on time and place. English Roundhand of the 18th century doesn't look much like German Kurrent. So the US Declaration of Independence is easier for most people to read than a random postcard from a century ago. Both because the style of cursive woudl be different, and because the latter is less formal and more likely hastily written.

The main downside to cursive having to learn to read and write it, which was considered worth it when people wrote much more by hand than they do now, which is why its teaching is questioned in places like the United States among others. Printing is not 'more modern' though. Block letters are the original form of the alphabet, older than cursive by far. It's also odd to write like it's dead an buried while a substantial amount of people, even in the USA, still use cursive, while in Russia for instance, handwriting is almost exclusively in Cyrillic cursive.

Anyway, 'cursive' writing only means that the letters are joined. Although present day cursive is more difficult to read, all else being equal, than present-day block lettering, it doesn't mean every cursive is harder than every given block letter style. Blackletter can be rather difficult to read. Alte Schwabacher too Reading unfamiliar letter forms is difficult regardless of what they look like, and if you exclude that factor then a badly printed text can easily be harder to read than a neat cursive one.