Well, that was pretty much the start of this sort of genre. I think there was even initially an attempt to use tank controls in it, because resident evil devs or something.
Oh that's not the first time I'm reading something like this, but what about Severance then ? It was released even earlier than DMC1 and didn't have such problems. To me it seems like the root of all the troubles is that DMC is a console game, that's why there's no free camera, firearms have to be switched via menu, enemy encounters are extremely limited etc. I like the game, but everything good about it is caught in a tight clutches of said issues, it's even more annoying to deal with it when you know that it could've been better if the developers weren't set on making it a console game.
Severance came out a few months before DMC, by that time they were pretty much finalizing the game. So they wouldn't have changed the camera on such a short notice, and let's not forget that using free camera controlled by an analogue back in 2001 wasn't the standard common sense that it is today. Plus unfortunately even back then Severance wasn't in anyway a popular game, adding to that the fact that PC as a platform was still years from being a serious thing in Japan, and most likely Severance just went by completely unnoticed.
Also when it comes to Hack 'n' Slash games IMO you can divide them into 2 categories: the ones with relatively slow movement speed and high commitment attacks wich punish the player for being careless and impatient (like Severance, Dark Souls, Nioh, Mount & Blade, Mordhau, For Honor, Dark Messiah, etc...); and the ones with fast paced combat and low commitment that reward aggressiveness and speed (like DMC, Ninja Gaiden, God Hand, Bayonetta, etc...).
So while before Severance there were already some games like it, there was nothing like DMC before DMC.
The camera system in that game plus the emphasis on athmosphere and interconnected level design is also a relic from the game's early development as a Resident Evil game.
But yeah, most of problems the game stem out from it being the first in a new type of action genre and hardware limitations (or the devs inexperience with the PS2 hardware since DMC was of the first games for the PS2).
For example haven't you noticed that when enemies spawn, they are always enemies of the same type and not different (for example you never see marionettes and shadow cats in the same room, you only see either marionettes or shadow cats). It's because either the PS2 had some weak memory, or the devs just weren't yet good enough to to optimize the game for the PS2. This is also the reason why DMC1 is still the only game in the series were all enemies have both ranged and melee attacks. It was the devs way of going around this memory limition to make sure every enemy has a diverse enough moveset to challenge the player.
ninja edit:
wow holy shit, I got so carried away by this I didn't even notice how fucking long the post got