I can see the convenience of fretting hand - because there is the natural arc w elbow as pivot point - other than that . . . ? ? ?
(I'm only responding to your last question Nuuska, because the others are just way over my head!)
The reason I was interested is kind of boring to explain, but I'll give it a shot:
The longer strings on the bass side of a fan-fret mean you can tune the bass strings lower than on your average six-string without the strings becoming too "floppy" or losing power.
This interested me because I play only in open tunings (I've invented about 100 or so) and being able to tune lower on the bass end meant I could come up with new tunings, ones with a greater spread between the low E and high E strings. (Because, you know, 100 tunings aren't enough!)
It's a little like having a long scale guitar (or a baritone) and a regular guitar combined.
I don't like having to mix string sets. I can easily tune the low E (on a standard set of D'Addario EJ17s) all the way down to A on fan-fret guitars with no discernible loss of volume, while also maintaining a feel that's comfortable for me.
I like the Guild G41 (thanks Richard!) for the same reason. It's an oversized dread and the longer scale length means you can tune it way low too. But since the high end is the same scale length, the B and E strings can be pretty tight, and -- depending on the tuning -- that sometimes affects the feel.
I didn't jump into fan-frets without some cynicism myself. ("Do we really need another goofy newfangled thing!?") So I first bought an inexpensive used Agile brand six-string acoustic fan-fret. After playing around with it for a few months, I knew I liked the concept enough to start beating the bushes for a used Lowden fan-fret, one of the few high-end makers to offer them.
Before the pandemic Lowdens weren't crazy expensive. Now, though, its hard to find ANY Lowden, new or used, fan-fret or not, for under four grand, and some are three times that price or more. I bought mine at just the right time apparently.
The ergonomic factors, which are often the selling point of these guitars, turned out to be a plus, but, like I say, that's not what drew my interest initially.
(BTW -- I still have the Agile "starter" fan-fret and it's for sale if anyone is curious.)