You are fine for a level that requires you to collect a certain item and when you do get that item, you can't quit the game with the item but instead you have to complete that level inorder to get the item.
I am? When did I say this? That seems rather frustrating to me. :/
For example--if I may stray away from true platformers for a moment--I recently played an Android game called "Silly Sausage in Meat Land". While not technically a platformer, the experience of playing it very close to the experience of playing a puzzle-platformer. In this game there are two types of collectibles (unless I'm forgetting a third): keys that are required to get through doors, and gems that are used to "buy" checkpoints. Death takes you back to the last activated checkpoint, and one has unlimited lives. The keys are part of the puzzles, and as such respawn on death. The gems, on the other hand, remain collected whether you get to the next checkpoint or not.
Overall, I rather like this system.
What you're describing might be analogous to having any gems collected since the last checkpoint be deducted from my counter and respawned in the level upon death--which I think that I'd likely find rather frustrating.
Again, Platform games are for the most part very easy to play. How easy you ask? Easy to the point that all the player has to do is move to the right to reach the goal (or sometimes left).
... Plenty of platformers are rather difficult, as I recall. There's a fair bit more to be done than just "moving to the right"--there are timed jumps, keys to collect, enemies to kill or avoid, etc.
As I said, not everyone is equally skilled at platformers.
In the Super Mario games, certain power ups allow the players to skip huge chunk of the level and go to the next. How would the player learn this? Because the games make sure that you do learn how to use them by the time you get them. Its not hard for a new gamer to get into a platform game really.
I think that this depends significantly on the platformer.
I'll confess that it's been a long time since last I played a Super Mario Bros. game; I think that the last was Super Mario Bros. 3, and I'm not sure of whether I completed it. However, I don't think that I ever completed whichever Adventure Island game it was that I had as a child, while I believe that I completed Monster In My Pocket more than once.
I'm pretty confident that there are other platformers that I've given up on as a result of just not managing to progress.
Imagine a multiplayer game being played by a group of friends. One of the players constantly knocks of the other players in the game. Obviously, other players wouldn't want that player at all so they would quit the game immediately.
Or how about playing an online game where you choose a server to play the game. you find yourself incredibly weak compared to the hardcore gamers out there. Perhaps you need to try someplace else where you can play with other players of the same level as you. That here is discipline. You need to know where you are right now no matter how great or bad you are in games.
Those are social games: how you play affects others, and is affected by the way that others play. In a single-player game this element may not be present.
When I'm playing a game by myself, why should my play be disciplined? Why may I not just jump in and have fun if I so desire?
But not collecting stuff ruins the whole point of platform games.
... I'm trying to recall whether I collected anything other than weapons, weapon-powerups, and plot-items in Cave Story, a platformer that I very much enjoyed--although its difficulty was very near to my frustration point. (I actually did give up on it on my first play-through, as I recall--I would likely have enjoyed it more had it been a little easier.) I don't recall any other collectibles; if there were any, then they don't seem to have been sufficiently significant to me that I remember them.
Instead, what I remember most is perhaps the story and combat: blasting enemies, fighting desperately against bosses, and watching the narrative unfold. That's what was important to me in that game.
I do like collectibles, and I do usually try to get them in platformers, but they also tend to be one of the first things that I leave behind when the game becomes difficult.
For example, another platformer that I very much enjoyed was Iji. In that game, I made a point of getting all of the "ribbon" collectibles--perhaps especially because they affect the story--but I'm pretty sure that there are audio-logs and perhaps other collectibles that I've never managed to find. And I'm fine with that: I completed the game, after all.