While I agree that it'd be neat to see a game like REmake be made today, it's really unfair to call the new games generic. We live in a world where most shooters end up having very similar gameplay (usually it's all about shooting enemies in the head, or hiding behind cover). I love how RE4, 5, and 6 instead are all about intricate melee systems. I think they lean more towards being action games than shooters.
Also, I'd say Capcom milked the series to death back in the day. RE1, 2, 3, REmake, 0, and Code Veronica all use extremely similar gameplay mechanics. The only big difference between them was the level design and puzzle design. I think that's a reason why RE4 was such a drastic change in gameplay style. Reviews and sales were reflecting how overused the formula had become.
I wouldn't be opposed to them going back to the style now, but it doesn't make any sense. REmaster proves that a lot of people just can't handle this style of gameplay, and if they went back, I think we'd see all the new RE fans complain about how they've completely switched gameplay style from action.