Fog decks fall under category 2, burn with wand.
The only difference is for a fog deck you are stalling the game until your win con combo comes out, as opposed to a deck that relies on drawing any fat creatures to try and win. It's a specific set of conditons you need to create for yourself, and it takes time with a fog deck (or any combo deck)
A bant deck with a few cloudshift, archaeomancers and arbor colossus bores me personally. I've been playing dotp 2015 since its release mid last year, and I need to keep the game fresh by exploring the more unique styles.
Timmy decks have been done to death, the card pool encourages it but it's fun to explore outside of "my creature smash! yay!" etc
+1. Though "Kozilek Smash!!!" is also an occasional and acceptable win-con for Fog decks.
I also agree with the complexity argument. Surprisingly, I haven't yet played against a Fog deck, though I have played a few dozen games with my own, but I imagine it's incredibly boring to play against and seems simplistic from the other side of the table.
However, when playing it, it's actually pretty interesting and complex. As the Fog pool is quite shallow, split between three colours, and all have different levels of utility, you have to make a lot of calculations on how much damage you can afford to sustain (which requires a good knowledge of the metagame in predicting your opponent's deck's contents), when to Fog and when to draw, when to wipe and when to risk your small number of win-cons.
Playing it is pretty fun, and not the same experience as playing
against it. And I think both are reasons for it's lack of popularity. Most hate the deck from just playing against it, and those that try it out find they lose pretty badly by making all manner of misplays, so give it up. That leaves only the good players who do well with it, who piss people off even more by winning a good percentage, which creates a shrinking cycle of popularity.
On a side note, a friend of mine won a game that lasted almost 2 hours in Ranked with this recently versus a lifegain deck with Elixirs, Griselbrand and Artifact destruction. Magic hell to some - Magic heaven to others!
Personally, I'd much rather spend two hours and win a titanic battle like that than win 10 games in the same time where all I did was repeatedly play out my hand and press "attack with all" every turn. Again, that's Magic heaven to some, but boring as hell to me.