Re difficulty it depends on the game really, and what difference it makes.
If like Civilization or Age of Empires, harder means that the AI cheats quite hardcore, then no, I don't think it is necessary, or often even fun, to play hardest. In both of these cases it is also quite blatantly the case to cover up poor AI programming, as has been shown with the improvements in AoE2 HD on steam, and as is far too obvious and quite disgraceful in Civ VI.
By contrast, if it means that the enemy builds up quicker but at least seemingly without cheating, and uses better tactics in combat, à la StarCraft II, then I think it is good as a challenge, to a point. At least now there are videos of people completing such difficulties, and in that sort of game it usually isn't too hard to perform similarly - the campaigns don't require -that- high APM. My favourite example of that was learning to finish the last Wings of Liberty mission on Brutal, the no air version, by just building 50 or so siege tanks. Good times.
If like in older FPS games harder means tougher enemies but no additional ammo or health, then I think that the easier difficulties are there for us to learn the maps, and where secrets and such are, so that harder difficulties are possible and even fun. Marathon is my prime example; I've been doing yet another playthrough on Total Carnage and very much realising that I only really get through it because I know about all the secret ammo caches, weapons, and powerups along the way. Yes there are people that can do the whole thing with the magnum, or even fists only, but one of those I am not. But I like that design, because it increases replay value significantly, and you really become a student of the game.
By contrast if it means mainly that enemies are far more alert, better at aiming, and better at hiding, and tend to snipe you before you can even see them, à la Halo, then no, I don't think it is necessary or fun to play hardest. Sure people can, and I would like to be able to, but apart from anything else, I'm too old for this sh*t