Vampire Killer would like a word with you. It did exploration and multiple kinds of weapons from year one of the series. Even before CV2.
I don't entirely agree about emphasizing exploration OVER action and platforming. SotN had plenty of both. The only thing they did to nerf platforming was getting rid of death pits. I would have preferred if they had kept them, but I can also imagine people bitching about having them, too. And if anything, the action is more intense than any of the previous titles up until you level up. And THAT is where they fucked up the Metroid formula and the action.
Simon in 2 versions of CV1 uses main weapons other than the Vampire Killer. The Vampire Killer wasn't even part of the story until CV3. And speaking of CV3, let's not forget that as early as stage 3 you don't even have to play the rest of the game as Trevor. The difference in SotN is that you aren't given the option to switch back after you start playing as Alucard.
I did find the RPG elements a little odd at first, but even that does have roots in CV2 as Crisis mentioned.
I honestly didn't even think about Vampire Killer. I've never even made it thru that one, so I can't really say for sure. But the exploration/platforming/action was a lot more balanced out in Simon's Quest. In SoTN it really WAS more about exploring and find the items you need to get to the next section. 
The RPG elements were heavy in Symphony compared to Simon's Quest. You leveled up in SQ twice at the most and the experience system barely plays a role. In SoTN, having to equip items and having to worry about leveling up to increase your HP and stats so you can beat bosses/enemies is a big part of the game. If you don't pay attention to those RPG elements, you won't get thru the game. And once you get to the right level and get the right weapons, the enemies are little more than road blocks. The RPG elements are pretty dictatorial in Symphony whereas they were all but nonexistent in the classic games even when they were there.  
The platforming is pretty nerfed in Symphony. Taking out death pits removes most of the risk, and most of the time, it's merely an obstacle. The enemy placement doesn't make it any more difficult really, because Alucard has so many abilities he can use to overcome it. Platforming in Symphony is, in a lot of cases, kind of like those crank wheels in LoS, just an obstacle that's there to make for some busywork. There's really little challenge to it and as such it defeats the purpose of having it in a way. In the classic games, the platforming was tightly designed. Enemies were placed to make it even more challenging, but that doesn't really occur in SoTN.  
As far as the "helper spirits" in CV3 are concerned, they're not as good overall as Trevor is. Sure, you don't HAVE to play as Trevor, but he's the best overall character, so why WOULDN'T you use him? That's kind of a weak argument to make, especially as Trevor is the focus of the game in the first place.
I'm not really shitting on Symphony, but there are things about it that weren't really terribly "castlevania-like" at the time.