Tokyo_Bunny_8990: Older games like Chrono Trigger, Megaman, every Zelda except for a rare few, also dont have difficulty levels but have wide appeal among gamers.
Chrono Trigger can be too easy for experienced RPG players (though I note that Final Fantasy 7 is worse in that regard, not counting two optional isolated bosses that aren't even in the original Japanese release).
Early Mega Man games have some difficulty issues. In MM1, Guts Man's stage isn't well designed, as it throws you off the deep end, introducing a mechanic in a context where, if the player doesn't succeed multiple times in a row, the player falls and loses a life. Fortunately, the developers learned, and a comparable case, Ring Man's stage in MM4, is handled much better; the mechanic is introduced where you only have to pass it once and failure isn't a death, and then it builds from there.
In MM2, which (in its English NES release) actually *does* have a difficulty selection, there's another issue, and that's that you can run out of weapon energy. At this point, if weapon energy is a death, it can be painful to farm new energy to try again, particularly since, unlike in MM1, placed energy pick-ups don't respawn until game over. The final stage has a particularly bad example of this issue: If you don't have enough energy to defeat the boss (which is immune to the Arm Cannon, your only free weapon), you have no choice but to intentionally get a game over, which takes too long. (Basically, it's a softlock if you don't have enough energy to kill the boss).
Mega Man 4-6 require playing too many levels from the last save point (that is, the last point a password can take you) to the end of the game, making them pretty much not feasibly winnable unless you have a huge block of time to play, are willing to leave the NES on, or are using an emulator with save states.
Incidentally, the original Zelda *does* have a difficulty selection. If you name your file ZELDA, or if you continue after beating the game, you will be essentially playing the game's hard mode, where things are re-arranged, the dungeons have been re-done, and some new (and rather evil) mechanics are added. (I remember one of the dungeon items being in what is probably the *last* place a player will look, to the point where a player will likely think they've completed the dungeon before finding it.
Tokyo_Bunny_8990: I think there was also a case where you can beat one of the CoD or Battlefield levels without touching the controller on easy but the game becomes insanely difficult with grenade spam on its hardest difficulty (both scenarios being kind of unrealistic for its setting).
Final Fantasy 9's optional superboss can be beaten without touching the controller during the fight, provided that you have a good setup for that and are lucky, yet nobody (to my knowledge) considers that boss to be easy. (With noting that luck is needed, as this is basically an RNG boss, who randomly uses attacks like Meteor which does something like 110-9999 damage to the party, possibly killing everyone except the character who was almost dead (I saw that happen in a youtube video).