OK I will share my dream game: I want Animal Crossing but with a passive adventure/detective element. It would include everything in normal AC but if a villager mentions their garden gnome was stolen, for example, you can investigate, talk to people, and deduce its location (Phoenix Wright style). No fancy effects to delineate the detective mode, it's just something you could do by talking to people or looking in the right places.
If you make a false accusation then your reputation in the village will quickly tank and you'll soon be a pariah, and it will be many lonely days of picking apples and doing stupid errands and favors before it improves. You must be confident in your conclusions or you'll mess up your save file and all the time you've put in. But if you are good, everyone will start to regard you highly and your reputation will grow (and villagers you catch will resent you). The others may even treat you as a Sherlock Holmes and consult you for big problems, like a fossil boosted from the museum.
Not all crimes will be solved, or sometimes you'll know who did it but they got away because of the real time clock. Because there's a whole game beside, you don't need to solve or bother with every one. The puzzles should be actually difficult not baby-tier thinking. Some will have false clues to frame people. You should have to rely on what you know from your many days walking the beat around town talking to people to have regular success.
Also there should be one really elaborate mystery of a big event from a long time ago that you can solve over the course of a year or two.