Generally, there are two extremes of (A)VN players: Those who see the game literally as a novel and usually dislike everything, that detracts from the experience of a standard novel (probably someone like you). Then at the other end of the spectrum, the players see a (A)VN still as a game and want at least some kind of interaction from the medium.
Obviously, I’m in the second team. That’s also why Funkelregen is a sandbox AVN, because free roam/sandbox elements give you (at least the illusion of) more choices/freedom. But of course I know the usual complains about sandboxes, so I went out of my way to make the sandbox as lenient as possible – no farmable stats, day-cycles, almost no events, that are meant to be seen more than once… And also I like the (programming) challenge of creating a working free roam infrastructure... (I'm probably weired...)
Among the games, you've mentioned, I have only played Headmaster and in a comparrison, my game has a far "easier" sandbox.