I guess here is also a cultural factor at play.
Some of us come from countries with rather different education systems in which written communication is taught differently from others. Therefore acceptance of other people's culture includes not only acceptance of their ideas and opinions but also of their communication style (and proper paragraphs breaks)...
And I did not even mention the use of a foreign language... Having had to learn English, I could do with some indulgence from native English speakers in those matters.
I travel a lot and can attest that there are cultures which are made more colorful by people who are able to talk non-stop for minutes on end. Those folks must have an extra set of lungs.
Of course, I rarely totally understand what they're saying.... ;o)
On a more serious note, I (and I suspect others) have some difficulty reading off a monitor. One can't easily mark their place with their finger while they digest one thought before proceeding to the next.
Placing a blank line between thoughts provides a 'thinking place'.
(When you used the word "rude" I assumed you to be British. What is your native language and do you not use paragraphs when you write in that language?)