Who cares about combos? There is nothing rewarding about repeatedly mashing buttons. There aren't any stakes in those regular action games. Dying means nothing in them. Enemies are just fodder and bosses are mostly just setpieces. You only play them to see cutscenes or the ending credits.
Compare that to losing 800k souls/amrita because you got too greedy and made a mistake. Regular action games can't replicate that feeling.
Souls games come with stakes and misery. Every enemy is a threat. Not knowing whats around every corner is the adventure. Traps and enemy AI are an actual thing.
Items, loot, armor and builds mean so much more in Souls than any regular hack/slash action game.
Look at what AssCreed gameplay has turned into.
Look what Team Ninja did with Nioh.
CDPR straight up said Dark Souls was a big influence for Witcher 3.
Look at God of War. It literally abandoned the old boring hack and slash genre in favor of a more new/ fresh Souls like combat.
All the double AA and B games inspired by Souls.
All the indies. etc etc.
It is absolutely its own genre. At this point I would say Dark Souls is 100x more influential in today's industry than any DMC or Bayo game.
I disagree with a lot of this, including your premise of the "importance" of dying. I actually prefer the combat style of the slower games like AC: Odyssey and Dark Souls, but I really hate how the DS games disrespect your time. Bayonetta is probably the only combo-heavy action game I've enjoyed till the end, and it was absolutely hard and move choices / item choices mattered a lot, but the checkpoints were largely respectful of your time, if you failed at something you didn't have to wade through 15-30 minutes of stuff you can easily wade through again.
The older DMC games I disliked because every enemy felt like a HP mountain, Bayo balanced it a bit more, and maybe the newer DMC games are more towards that end, I'm not sure. DS has a mix of both, but the thing that keeps me from playing more of those games is simply the terrible checkpointing system. You say it makes it more threatening, and seem to give it more meaning for you, but I totally disagree. Having to replay and refight the exact same path and fight 1, 2, 3, however many times is not meaningful, it's pointless. One of the things I like about AC: Odyssey is how dynamic the encounters are, there's only really like 3-4 kinds of enemies but the terrain / amount / layout / traps / your loadout dramatically change how one fort plays from another fort, and you never really need to do the same fort twice, if you die you have to redo some but the game is so screwy you might not
I enjoyed the old God of Wars as much as the new one, although I can respect the new one is incredibly more refined and polished and a much better story teller. The new GoW is also way better at respecting your time than the DS games. I can't really debate the influence of "slower" 3rd person action games vs "faster" ones, because the history of video games is incredibly broad and the influences can be hard to track and I don't feel like digging into it. DS certainly has had an impact, but I don't really agree that DS is a different genre than DMC anymore than FF6 is a different genre than FF12 or Diablo 3 is from Path of Exile. It's a different sub-genre maybe, sure.
Now, all that being said, about 90% of this is personal opinion and preference. Influence is something that could likely be tracked down but I would bet you haven't put in any more research into it than I have, but I wanted to contrast your absolutist statements with my own perspective as someone who enjoys the core mechanics of the Souls-esque games but doesn't play them because of their other design choices, and similarly has issues with most of the more combo-heavy action games. GoW is largely the exception for slower ones and Bayo for faster, for me, in that they both fulfill the excellence of the core gameplay while not bogging it down with unnecessary grinding (in combat or otherwise) or wasted time.
You mention Team Ninja, but choose Nioh instead of Ninja Gaiden, which was the hella hard game of its day.
Bayo and DMC are not "regular." They were, are genre-defining. Bayo, in particular, gets 10/10 gameplay. They are not beat-em-ups like Streets of Rage or hack and slash games like Diablo. Weapon builds change how you take on enemies and bosses. Underestimate an encounter, and you die.
The only real difference between Demon's Souls (which, I always laugh when the point of reference is the sequel, rather than the PS3 original, because that's always a dead giveaway as to how hardcore Souls fans really are) is what appears to be the atrophy of experience points upon death. But those can be grinded back, so nothing is really lost...except interest in the game because now you're grinding.
The only real impact is psychological.
Sekiro improves upon the DS formula by turning back toward fast-paced action. Now, you can get your "negative growth" and intentionally indecipherable story without the game moving at a snail's pace.
This is another good perspective on it. I died a ton in Bayo vs normal fights (more than in GoW, even vs. Valkyries) but it was OK with me because you just got dropped back into that fight and could use what you just learned. Grinding in SP games is always a delicate balance, it either needs to be entirely designed around it (e.g. Minecraft, where all you do is gather stuff to build stuff) or it needs to be minor at most, otherwise why does it even exist?
Edit: I complain about grinding and retreading as someone that love metroidvanias and tactics RPGs, the first of which has inherent backtracking and the second of which usually rewards grinding. The difference in metroidvanias is that when you revisit an area, it's with upgrades and you are exploring and you are usually stomping on stuff that used to give you challenge, and it's often optional. For grinding in tactics RPGs, it's usually optional to unlock more flashy skills or classes or something or to mess around with new builds. In both cases, dying and being forced to redo something you just did always sucks still and you want to avoid dying even in the same room you restart in.