I really like that idea. One could argue that Wrath of Ashardalon or Temple of Elemental Evil are already "D&D Boardgames", but that's not really true. Those games are merely about the least-interesting part of D&D: the tactical grid-based combat. A D&D board game should instead focus on heroic questing, clever solutions to interesting obstacles, and roleplaying.
I agree - except that the history of D&D shows that roleplaying naturally emerges from a tactical combat game where each figure is a person/character. So - you need to enable the roleplaying rather than force it. All that takes is to say - "now this happens" [unexpected change on the tactical grid] "what do you do?" - and you are roleplaying.
Tossing a textbook (the PHB) at a newb, or sitting them down to the current nothin'-but-combat "board games", simply does not suffice.
It's a game with one page of rules for the player to look at - or in our normal terms - the character sheet.