I haven't solved a puzzle in months, however, when I was solving I managed to solve a Fiendish in roughly 3 days without any sophisticated solving methods at all. Can't speak for anybody else, obviously.
Without resorting to coloring, forcing chains, trial and errors, computer programs, should I be able to solve the harder puzzles?
I don't know. My impression, from what I've read on this site, is that Hard and above need the advanced techniques to solve them. Since I've never gotten that far I can't really say (I have yet to master any of the more sophisticated solving methods and am not sure that I want to). I'd like to be able to solve any puzzle that comes before me without bursting my brain learning the advanced methods but I can't, so I can either choose to learn these methods or stay in the Medium category (or not solve at all), depending on the level of entertainment I would like to derive from the puzzle. And that seems to be the key to me - level of entertainment derived from the puzzle. I'm not sure that I really want to study that hard in order to learn how to play a game.
The challenge, it seems to me, is with the self. The puzzle is a game, entertainment, a past time. If you want to get faster, then do what it takes to achieve that. If you want to learn the advanced techniques then do that. If, however, walking the dog is more attractive then that's what I'd do.
The beauty of this puzzle, as far as I can see, is that these choices are there. For me, I can advance, or not, as I choose.
Luna