If the Doctor was trying to pass as human without a daemon, I suspect many people would generate their own explanations for why there wasn't a daemon immediately visible. The expectation that people have daemons is so strong I think they'd be unwilling to believe the lack of daemon before their eyes, since the Doctor is clearly not damaged like people who have undergone intercision and he's too male to be a witch.

Gallifreyans living outside the Citadel are shown wearing furs, which presumably they hunted themselves, so they at least have large furry animals. ...Or possibly large furry vegetation.

LOL! Way to think outside the box. I also support your assertion that daemons are fun.