My first thought was "if the owner of the driveway is fine with you blocking it, why can't you get permission to just park in the dingdangety driveway?"
That said, I think this is one of those times when it's not rude to ask but it's also not rude to say "actually, I'm not going to go along with your request." I do think the letter came off a bit entitled, but I'm actually willing to give that a pass because most people aren't quite as eloquent on paper as they might be face to face. The letter writer did request politely and offer an alternate solution (assuming there really are six spots regularly free around the corner), and I'll give him/her the benefit of the doubt and assume the letter was for this ONE car which presumably parks in that spot a lot and not, say, every single person who ever visits a friend in that neighborhood and happens to park there. If it were me I'd probably be annoyed at first, then make an effort to park elsewhere most of the time. (Not "always," but "as long as I don't have too much to carry and there's another spot nearby and it's not raining or snowing and I'm not hauling a toddler.")
I'll admit my experience may be colored by when we first moved to our house - our very first day, literally while the moving truck was in our driveway so we were parked on the street, we found a note on our windshield asking if we could please park elsewhere. I was really miffed about it - for about two days, until I realized how hard it is to back out of the driveways on this street. If someone is parked opposite your driveway in *just* the wrong spot, it takes an eighteen-point turn to get out. I assume our neighbors didn't realize our car corresponded with the moving van, and/or were frustrated with other people taking that exact part of the street. We pretty quickly figured out which street spots are "safe" and don't bother anyone, and when we have to we use those.