I see both points but regarding (2), there are common cases where you are not necessarily doing anything wrong but the 80 character limit will make your code less readable, especially when using four spaces or more for indentation. For example you might end up in the fourth level of indentation wanting to write a list comprehension that would be perfectly readable in one line but have to break it down because of this rather short hard limit.
I think having a soft and a hard limit makes more sense, if anything, I would make 80 characters the soft limit and perhaps 100 a hard limit, although I'd prefer them to be 100 and 120.
If you're in the fourth level of indentation, you might already have a readability problem.
"Might" being the key word. You might, if you are writing a simple script, but if you are writing some more complex code, class and method already take two levels, and that is your base line, I don't see how having two more levels is a readability problem.
1 - yes, screens are huge, but it doesn't mean people can/will use small fonts or will scroll the screen
With today's big/wide screens it's more useful to have code side by side.
2 - Abuse. The 80 character limit is a pretty good indicator that you should be doing something else instead of having your code go over 80 characters.
Long lines are confusing, and you most likely can split the logic in several lines, facilitating maintenance.