personally, I think it makes it a lot better when the influence of the original personality/character is clearly present or stated to exist. Makes their actions make a lot more sense honestly. In cases like Magic stone gourmet, his concern over his father like liking him or his mom feels out of place since he's mentally an unrelated grown man that was reincarnated. On the other hand, in Otome game mob villian, his disposition makes sense because he didn't reincarnate with most of his memories, only with a little about the game and nothing about the person he was. Not only is it fine for him to act immature, things like him getting engaged to another little kid and going all 'wife guy' with her and constantly telling everyone all the things he loves about his little wife, it doesn't feel odd but cute even. After all, he IS a kid, both physically and mentally. He's just a clever kid that got specific and useful info on what was making his family miserable till now and how to fix it. He isn't even the only oddly clever kid, alot of the other kids that work with him later, his wife and sister included, are pretty precocious, basically making it a trait of the better noble kids.
But, yeah, it makes the mc and story make more sense if the original personality is still partly or even mostly there. It's always way too much of a stretch that the office worker game otaku becomes a death-defying action hero for the sake of what is probably the 5489230th iteration of a character type they've seen rather than a native fighting for their own very real life and loved ones.