It's not just all that's been said, allthough q3 is right about not using gods = forgoing a huge resource. Not just huge resource, but a pretty dependable huge resource which you can plan around.
Vicious lets you really see what the gods allow you to do, and how much easier it is with proper understanding of them. And piety generation, desecration benefits and all that plays a part in that. The original Naga City had you locked in with nine altars and ten bosses - any you could do it. Heck, I never even abused transmutation in there even back then. I could not have imagined by that point (without expirience with old Gaan'Telet and hundreds of hours sunken into it), that anything in the game is that powerful.
If anomalies like rogues, monks, triswords and such let you get through everything else you never get to see just exactly how powerful gods are, how much you can push them and all that. This is one of the reasons (edit) vicious fails as post-endgame, because what vicious really teaches is just how much power you are forgoing if you go faithles, and you're supposed to be learning that to a degree before you do them. Otherwise they're just a stepping stone.
Also, wamonger being sort of as hard as faithless is directly related to piety generation - warmongers have trouble worshiping piety farms like binlor, mysterea and JJ, have little interest in worshiping EM, have trouble worshiping TT to a degree, and only really work with GG, Taurog and Drac in certain combinations. (The other reason is that many classes are glyph dependent).
Miser or hoarder, on the other hand are also worship restricting badges - they lower the finer points of Mysterea because of limiting refreshment (hoarder), taurog because of inventory space (hoarder), drac and gg because of no conversion / lower ammount of conversion fodder (miser, hoarder), and so on and so forth.
And Tinkers are as good as they are for me mostly because all the extra items and gold makes them get more out of gods than other guys would by letting them use the boons more effectively, or gain piety more effectivly through conversion fodder. (Well among other things). Wizards can actually time their glyph conversions the best because they can get the glyph CP benefits while still having glyphs to use for refreshment, for example. (Not their strongest point, but it's there).
I almost got pwned by Shifty Brickwork!