Cave Story has an energy bar instead.
The bit about Cave Story was an aside--it was simply a case in which I might have had more fun had the game been easier; in any case, I still don't think that one needs either lives or an energy bar.
More to the point, you said the following, referring (I believe) to platform games in general, not Cave Story in particular:
What would make the game any more challenging if lives were removed if I respawn from the last part without going to any check points?
My answer, in short, was this:
Remember, it's not necessarily true that all players want the game to be more challenging; some may well want it to be less so.
Also if you find it difficult, have you considered getting health upgrades or saving that heart pot for the final boss?
It's been a while since I last played the game, but I don't think that I squandered my resources, at least given my level of skill. I think that I recall that I gave up on my first playthrough well before hitting the final boss, becoming frustrated while trying to defeat Monster X (I think that it's name was--the cat in the tank, at least). I did eventually deal with the final boss, and even (with the help of a guide) managed to defeat the bonus boss, as I recall.
... its good enough because of how easily you can get a lot of better equipment in the later half of the game and that's what I mean with the collectibles.
If you've read a guide, at least--I don't think that I'd have discovered the better powerups for the initial gun, let alone the means of saving Curly or getting the upgraded jetpack, without reading information on the internet.
That's the thing that platform games need. Either make the collections act as power ups or give rewards that are worth having. like a congratulations poster or unlocking a bonus mode or additional concept art, etc.
I suspect that what makes a collectible worth having may vary from person to person--some people might be happy with little more than an increased score counter, or an achievement. For myself, I do prefer to have something more than a blank number or a meaningless achievement.
(Funnily enough, my favourite implementation of the "achievement" mechanic was arguably that used in Planescape: Torment--the tattoos were in many cases essentially achievements, but unlike the standard sort, actually provided optional advantages and disadvantages. I don't think that it was a perfect implementation, but I do really like the idea.)
I'm also not convinced that all platformers require collectibles. Personally, I do like them, but I suspect that there are players who would be quite happy with little more than platforms and enemies.
In any case, I don't think that the inclusion of powerups--especially the sort that unlocks external rewards like posters or bonus modes--relies on the inclusion of lives.
You just mentioned that having lives makes it hard because of every gamer not being skilled at certain things where as having hard levels later on in the game without lives makes sense for those not skilled?
I'm saying two separate things. If I recall correctly:
First, you claimed that the removal of lives makes a game easier. In answer to this, I argue that it's possible to make a game challenging even when using unlimited lives.
Second, you claimed that making games easier makes them less appealing. In answer to this, I pointed out that this isn't the case for all players.
Put another way, I'm saying that some gamers prefer easier games, and that, even for those that prefer difficult games, the use of unlimited lives isn't necessarily problematic.