To me, the hobo phase is the most fun part of any game with rpg elements. It is the only one where I feel like I'm not cheating, as leveling up and upgrading stats is like managing a difficulty slider as the game grows more demanding.
But can you actually play low level, or low stats enjoyably? Stat points have become ubiquituous and there's hardly an action game or shooter still lacking them, let alone actual rpgs. Have you ever ignored these systems and focused on the gameplay alone, anon?
Hard mode: something other than Dark Souls.
In my experience, Xenoblade and Yakuza suffer a lot from overleveling, but you can't really gauge the problem unless you compare games in a franchise that introduced stats, altering it's balance of challenge (Castlevania).