I'd be happy with if the player has, say, 5 lives per checkpoint. Whether you die 0 or 4 times on the way to the next checkpoint, you'd have 5 lives after activating the next one. (See LittleBigPlanet 1 on PlayStation 3 for an example.)
This way, dying too much at one section will put you back to the start of the level, so there's still an incentive to not die, but you'll not be disadvantaged (nor advantaged) further the next time that you get back to this section after a game over.
I want to agree with you here, but I'm not yet sure how well this would work in the context of SRB2. My first impression of this approach is that it should work very well for games with streamlined level design, such as crash bandicoot, but I have no idea how well it would work in the context of a game with more open, exploratory design. I would like to test this out sometime soon as a lua script.
TL;DR: I think that accumalable lives punish bad players, since if they die too much, they may have to restart a level with less lives than they started it with at first.
While you have a point, I believe that you are overlooking an important advantage of accumulable life systems. When new players encounter sharp difficulty spikes, they have the option and incentive to retreat and gather more lives before returning to those challenges, allowing them to tackle them later with more lives, and more importantly, more skill than they had initially.
SRB2 may not capitalize on this feature as well as it might, however. Players are unable to or load a save in a previous level until finishing the game. While this certainly prevents farming lives - which can be a definite problem in some games with accumulating lives - it means that new players must begin the game again from the very beginning if they seek to tackle that challenge with a greater number of lives.
That being said, I don't think that having to restart a game to return with more lives is necessarily a bad thing. As I mentioned above, by re-doing the earlier portions of the game, new players can better establish their basic skills and experiment with more advanced ones in a safer environment, all while preparing for the more difficult one that they know is coming. By returning to these earlier stages, players get the opportunity to explore more of the levels than they had previously explored and, in this context, will have greater motivation to do so. These returning new players also have the motivation to tackle challenges that they may have skipped in their previous runs in order to find and acquire more life monitors.
In my own experience as a Sonic newbie, I could hardly beat the second zone of any of the genesis games for some time. In Sonic 1, 2, & Knuckles this would result in me replaying and winning in GHZ and EHZ repeatedly until I was skilled enough at the games to consistently overcome MZ and CPZ, respectively. As I did so, I was driven by my desire to overcome the next levels to overcome optional objectives in the first zones to aquire more lives. I felt that I needed these lives to beat the next zones. In truth, I needed the skill that accomplishing the optional objectives caused me to develop.
In Sonic 3, however, the save system meant that I had the choice to either keep grinding HCZ until eventually I could beat it, or begin a new save and start again from AIZ1. I usually opted for trying again from AIZ. I both enjoyed AIZ more at the time than HCZ (I still do, to be honest), and I hoped that, if I played it well enough, I could enter HCZ with a bubble shield and enough lives to make it through to the following zone, with similar results to S1, S2, and S&K.
Not that I would advocate for abolishing the save system in SRB2 by any means. Please don't misinterpret this post as such. I'm establishing the strengths of accumulating life systems right now, not trying to paint save systems in a bad light.
Is "the number of Game Overs" permanent per save slot, or just temporary until you beat a level? In the former case, I disagree; That's a negative statistic that can never be decreased (aside from deleting the save slot and starting all over), which I'm not a fan of, as that makes it possible to make a save slot permanently "not perfect".
I completely agree with you here. I've never gained anything but embarrassment from being told how many lives I lost in a game, and don't understand the appeal of the system.