It really depends on the game, the genre, and your skill in each, really.
For Doom, I play on Ultra Violence, as Nightmare is basically the same thing except that enemies respawn constantly if I recall, which is tedious. That being said, it indeed wasnt challenging enough. I ended up barely doing much actual shooting; as there's berserk packs somewhere on nearly every level, I mostly just punched everything, which was hilarious. Except things like Barons or similar stuff that just takes too long.
Alot of games though, yes, I just pump the difficulty up immediately, and I do very well. Or even with competetive things like fighting games, I'm typically very strong even just starting out against others.
Though, put me in a MODERN FPS, and well, it's not one of the genres I do well in, that's for sure. Can handle all sorts of games these days at their toughest.... but those? Cant hit a damn thing half the time.