The thing I personally miss the most in Ecchi Sensei is the ability to decide for myself, OK let's say it's day 6, and what I want to do is go to the gym in the morning (where random events MAY happen) and then romance Sloth-chan (insert any other character) today, because that's just what I want to do, even though according to the script I might be supposed be going to an anime-con or whatever.
That ability to spend time with the character you're really into, when you want to, would be groundbreaking. Also a little bit of micromanaging your life and stats would be great.