I know little about paddle boards. Here are some thoughts, though.
To go faster than displacement speed, you will need to plane. You can easily plane by surfing down a wave, or attaching some sort of sail/kite, as proved by surfers and windsurfers. I believe it would be very difficult to plane under paddle alone - particularly to sustain a planing attitude during the recovery phase of the stroke, particularly when such a long paddle is used. There was a hydrofoil kayak that allowed this, but it was with an extreme high-angle racing stroke.
So, if SUP's have to follow the same laws of physics, I'm thinking a 12' board will indeed be a bit pokey, especially when compared to racing kayaks/canoes which have l/w ratios that surpass any SUP i've seen (though I haven't seen many). Put another way - the higher your centre of gravity, the more stable your craft will need to be, which means it will need to be wider, which will mess with your l/w ration, unless you lengthen the craft, which will mess with your skin friction and maneuverability.
I'm not against paddleboards if people want to have a bit of fun. However, I see them as beach toys more than boats, and find the industry push to use them for tripping and racing and whitewater and such to be a bit silly.
Bent Shaft Canoe Paddles