I grew up in canoes, and have both canoes and a kayak. They do different things. A plastic kayak is easy to toss in the back of my truck without having to deal with a roof rack, and I can literally load it up and drag it a quarter mile along the shore instead of carrying it. I wouldn’t do that with any of my canoes. A full size canoe is also really difficult to manage in the wind if you’re in it by yourself, even sitting in the bow seat facing the opposite direction it usually puts the other end of the boat in the air and it functions as a weathervane. Trying to quarter into the wind is about as frustrating as it gets under that condition. I think with two people a canoe is a far better option, but there is something to be said for a 12 to 14 foot open kayak, something like a native ultimate or similar, that is fairly stable, still has plenty of room inside, but really easy to transport and deal with wind. There’s also solo canoes like the 12 or 14 foot discovery models or similar, which sort of split the difference and can be paddled like a canoe or like a kayak. They are pricey, but I sort of drool over some of the high-end solo canoes like this, I think they would be great for hunting. I had a 15 foot solo canoe for a number of years that I sold a decade or so ago, would’ve made a great hunting boat.
Paddling my little kayak with a small pack, a bow, and a deer would be humorous at best. In a bigger boat you can just load it in, assuming you can lift it yourself. Otherwise I’d be tempted to quarter it out before putting it in a small boat.