Mostly not, no. Because often enough it's just a power fantasy, take RE4 for example, the game has pretty much the perfect skill progression throughout the game, and then New Game+ just has you rushing through your game with all upgraded, powerful weapons and a fully upgraded health bar, basically no effort. Especially as you can't switch to a higher difficulty. Other games take this into account, like Bayonetta and DMC1, where New Game+ switches to the now unlocked Hard mode and as far as enemy encounters go, the games basically continue where the Normal run ended, throwing end-game enemies right at you from the very start, so you kinda need all your previous weapons and skills until you really mastered the game. There are also a lot of skills and equipment you won't unlock during your first run that flat-out change how you play the game.
And then there's Dead Rising, which is completly designed around multiple playthroughs with stat progression and it's flat out not a very fun experience during your first run without speed upgrades and some useful melee moves.