So, a big part of many games, especially action-adventure games is getting the player to identify with the player character. While there are a lot of techniques to this, one that is often taken for granted is making the main character humanoid, just like the player. Certainly there are diversions from that, as you said, but generally... people see themselves as people, and then because of that, there are considerable resources dedicated to and designed to make playable humanoids possible, and a lot of people in the industry have experience and skills in playable humanoids. Playable, say, quadrupeds? Not so much. In fact, many of the design assumptions you might have, from object interaction, to talking to NPCs to who knows what, all go out the window.
I think Okami did something really marvelous, and it worked, psychologically, for two major reasons. 1) It was about the gameplay. Okami would have lost much of its charm in different genres, but as an action puzzler the character is already abstracted to a tool. 2) It was a highly stylized world, and based on a well-known myth, so there was a lot of freedom to explore that concept. 3) It was a canine, and many players are used to humanizing and empathizing with canines (sometimes better than other people). Add to that her cat-like agility, another familiar domesticated animal, and Okami has a familiarity that isn't TOO far off from a humanoid.
The other barriers, I suspect are that playable animals are associated with "kids stuff" and if not that, with the "Furry" culture, which is, among other things, overly-sexualized.
I mean, I'd be intrigued about a game where you play as a dragon, instead of a guy with a dragon, but what, exactly would be the gameplay? You're not platforming. You're not performing combos. You're not getting ambushed by rival factions. Or are you?