I think part of the reason people view the life system as archaic is it's not implemented in the same way that it used to be. Before, losing lives would basically reset your progress in the game completely (much like it would in arcade cabinets, necessitating quarters to play again). Nowadays, getting a game over resets your progress in a particular level so you have to start from the beginning. There's a few problems with doing it that way:
- Some levels are so short that losing your checkpoints doesn't actually feel like a major loss of progress at all. This will make levels feel rather lopsided; some levels checkpoints are negligible while others, checkpoints are important. On top of that, more difficult level design often entails making checkpoints sparser, at which point dying normally isn't very different from a game over.
- Some games/levels straight up don't have checkpoints... In which case, a game over is no different than just losing a life.
- Some games don't really have levels in the traditional sense, making it difficult to determine what would be considered a reasonable amount of losing your progress to game overs.
In the cases of checkpoints hardly mattering or no checkpoints at all, there's no point in having a limited amount of lives as you would lose the same amount of progress either way. In games that don't have levels, implementing limited lives would be difficult. Either way, the less arcade-y structure of modern games makes it difficult to justify having game overs in them because they don't serve a purpose that's any different from simply dying in the game. The only way that would make them distinct, to bring them back to their former glory of completely erasing your progress in a game, is an unpopular design choice and reasonably so — by doing it this way, players will have to go back through levels they already previously completed, which is frustrating and tedious rather than fun. Players put up with it in arcade machines because there simply wasn't getting around it, but now that games implement far less frustrating life systems it would stand out like a sore thumb in today's games.
This is also not to say anything of the fact that gaining extra lives in games that
do still implement game overs is pretty trivial, and often players don't even experience them anymore. When a game is that forgiving, the game over is just extra fluff that is taking up time and space to program.
Simply put, games today are either too forgiving or too structurally incompatible for game overs to complement modern game design. Putting the game overs of old back into games isn't going to be a popular solution, either, because games have more consideration to accessibility these days, both in the amount of time people have available to play them as well as difficulty, and game overs of that nature fly in the face of that accessibility (not to mention are just... really, really tedious. seriously, why do I have to replay the level I already beat because this one is providing a hurdle?). You could probably try it with an indie project, but it's likely going to be niche among retro gamers rather than something the general populace is going to go for.
I also personally think trial and error isn't a bad way to play the game. A game is supposed to teach you how to play it, and if you feel you have to try again and try new things each time, then it is appropriately punishing you for making a mistake. In fact, if you get rid of game overs entirely, you can actually design harder levels that may take multiple attempts to figure out without creating needless frustration for the player upon losing progress. Without the looming threat of losing your progress, there's less of an impediment in experimentation, which in itself can be a fun way to play a game, especially since it invites you to try things in the game you wouldn't try if a game over was looming over your head. This in itself induces creativity.
Of course, that can be done wrong, and it's most notably done wrong when trying to guess, say, a numerical password. But for more complex puzzles, futzing around with it can be a perfectly valid way to play it.
I find if you're unable to get invested in a game because of the lack of game overs, I don't think the lack of inclusion of a game over is the reason for it, but rather that the game is not designed in a way that gets someone invested. Game overs can't fix weak puzzle or level design.
