Would it, though? Being able to roll around and ground fire at, slide into, kung fu fight, and wrestle everything in sight seems like it would only trivialize anything that could possibly pose a threat in REmake's setting. Certainly wouldn't count as a horror game anymore so much as an action game with horror-themed enemies.
I'm of the opinion that monsters aren't what makes a horror game scary. Despite being a huge Silent Hill fan, the enemies rarely ever bother me (despite being brilliant, artistically and how they impact the narrative), and Resident Evil, apart from the slower, more puzzle-oriented design of the earlier ones,
were more or less action games with a horror theme. My problem with the newer games is the considerable lack of said horror thematics. A game with the gameplay of RE6 but the actual thick, claustrophobic atmosphere of the earlier games would be awesome to me.
It's always the setting, sound design, and atmosphere that gets to me; not so much the enemies. Just because your character can be a badass and perform a lot of actions doesn't mean it has to have a military shooter vibe. Resident Evil 5 was huge on action, but when they made that Lost in Nightmares DLC, while not particularly scary, the atmosphere was on point, there were puzzle/collection elements-- and there for a little bit the whole damn thing felt right at home.
The part near the end, for example, when you lose your gear and there's some huge bastards down in the trap with you and you have to use some cunning to get around them and get back on track; despite playing as a human gym, it was very intense because they put a little thought into it and the atmosphere was awesome. You can have plenty of sections like these, puzzles, slower moments, and great atmosphere despite your level of badassness.