Well it will, but I think that's just more natural than anything. Also keep in mind, as we get older, we get scared less. There was a time in my childhood I couldn't even play RE2 by myself because I was scared of just walking into the Police Station rooms or getting Lickered. Now (whenever my PS2 actually decides to let my controllers work), it's not a big deal. Things tend to be less scary as life goes on.
Also, the limitations of older games actually helped lend to some of the atmosphere, like the tank controls, crappy camera angles, and limited saves. However none of the three are really acceptable in this day and age. I mean, you shouldn't have problems controlling your characters, fixed camera angles are rarely a good thing, and limited save points are a pain in the ass not so much for the actual game, but then finding time to actually play.
The Save Thing I think can be fixed by something already used. The Kingdom Hearts: Chain of Memories Save system. Basically, you had your limited save points (though you'd actually create them, but that's not relevant to this point) which you'd get your normal save system. HOWEVER, you'd also get a Quick Save where you could save at any time. However, it'd automatically send you back to the main menu and would only let you continue that game and if you died or just normally quit out, you'd go back to the place of your actual save, not your quick save. I think that system works. Have actual save points that will help give consequences to losses and such, but have another system in place in case you need to bail in the middle of something.
But yeah, it's gonna be hard to sell the horror genre, just because we've seen it all at this point.