I don't see this as a universal truth. Someone who played in dozens of AD&D campaigns over the course of many years hasn't fully played the game because the highest level attained was 11th or so?
An open ended fantasy game cannot be objectively "fully played" unless said game has a defined end. AD&D for example has no official level cap so it can never be "fully" played at all.
Yep. You don't understand a lot of the rules decisions until you see how they do, or do not play well at the higher levels.
Like, one example that stands out in my minds, is everyone talks about how god like mages are at higher levels. I found them to outshine fighters, etc... in games where the DM was afraid to give cool magic items to the other PC's. I found mages very easy to kill at higher levels, especially if a fighter had an item giving them an Anti MAgic Shell. Hitting mages with magical arrows, multiple times, from multiple fighter types, kills them pretty fast too.
So, as I see it, people claim the mage is an all powerful god because his spell list makes him look like one. However, when you actually play the game to those higher levels you figure out strategies that keep the mage pretty easy to kill. Plus, as the Game Master, you see the reason for allowing such things is to keep the mage in balance.
Heck, in 3E, the SR's, resistances, and immunities effectively turn Epic Level mages into buffing machines, because the opponents were immune to fire, acid, sonic, hold, charm, etc...
Which shows how 3E actually needs to tone down on such things at lower levels to make higher level play actually more viable. Which you will never see unless you play into those levels. My two experiences were to the 68th and the 48th levels, and in both games the Wizard class sucked at above 25th level.
So yes, I think it is important to play the game to its highest levels to really get a grasp on how its rules work and hold up across the levels, or don't.