And there was considerable debate prior to the referendum within the Leave camp as to whether to go for a "soft Brexit" (close regulatory alignment) or "hard Brexit" (what the final deal ended up being).
Indeed parts of the leave movement explicitly used as an argument that a soft Brexit was possible, including explicitly airing the possibility of a Norway-style EEA membership. Given how close the result was, it's highly unlikely that there wouldn't have been greater support for a very soft option than for what we got.