I think you could argue the reverse, if anything, though I still think that linebreaks are preferable anyway.
Let me take an historical approach to this.
We use space and punctuation and typography to chop up written discourse into digestible units. Once we have these units, we use our thinking to build up a model of how those units fit into a rhetorical structure: what is a major point and what is minor, what is a supporting point, what is incidental, and so on.
Those devices are specific to written discourse. Spoken discourse has its own devices—including volume, gestures, eye contact, and pitch—to make the structure of what is spoken clear; written discourse did not have access to those devices, and has had to put up its own equivalents.
In antiquity, those devices of writing were rare to non-existent. There were no italics in Ancient Greek; everything was in all caps; punctuation was invented late and used grudgingly. Several ancient scripts used mechanisms to break up words; Greek and Latin were not originally among them. Recall the new-fangled fancy grammatical terminology that Euripides uses in Aristophanes’ Frogs, including sentences. To his old adversary Aeschylus, there are only epea, utterances, which can be as short as a word or as long as the Iliad.
All this made reading laborious. And that was OK: the number of literate people was small enough that reading could be an elite skill, and the culture of literate people was homogeneous enough that they could fill in the blanks (actually, the non-blanks).
The Alexandrians came up with punctuation and paragraphs, though there wasn’t much spacing involved originally. The notion of the punctuated sentence and phrase, and the spaced word, were stable in mediaeval times; the paragraph reinvented via the pilcrow (¶). By the mid-Renaissance, the tools we now use to chop up written discourse into digestible units were all in place.
Those tools made reading less laborious; and with the advent of first printing and then universal education, reading became more widespread.
But stylistic convention still favoured the long, periodic sentence, by emulation of the Classics. Partly this emulated a time when an elite could take the time to pore over the long sentence, and work out how its bits fit together. Partly this emulated languages which had mechanisms for chaining sentences together, which made much more sense in Greek and Latin than they did in French and English. But the sentences are at least supposed to be periodic—meaning, with identifiable subunits and structure that fits together. If you just take the time to concentrate on the connectives, as both the links between the phrases, and (too often) the separators between the phrases, in the absence of generous commas.
If we fast forward from the 1700s to the 2100s, we are now in a time when long periodic sentences are avoided, in favour of short choppy sentences; when long paragraphs are avoided, and indeed criticised as unreadable, particularly online; and when the internal structure of paragraphs and sentences is often made blatant through dot points and indentation.
This is partly fashion, driven I suppose by Hemingway and modernism. Partly, it is that we have to read more than ever before, we have to read stuff we don’t read for fun and leisure, we need to skim, and we don’t have the patience to wrestle with long Dickensian sentences.
So. In the olden days, there was less white space. People had to look carefully for connectives and punctuation, be conversant with rhetorical strategies, and have a decent amount of cultural preparation, in order to make sense of the structure of written text.
Nowadays, there is a lot more white space. The building blocks of the rhetorical structure are much more obvious; conversely, there is much less signalling of what the connection is between the building blocks, via connectives.
I think this means that the vertical space gives people room to think about what the connections are—and they need the room to think, because some of the other structural cues are no longer used or presupposed. I also think this still causes less of a strain than the olden day long sentences and paragraphs did.
