Some of this code-screen mistrust seems to come from the flood of poorly-qualified candidates; maybe there's a more diverse pool than before, but it comes at the cost of lots of wannabes.
For remote developers I do deviate slightly and I actually ask them to do a little coding, but that's because it's always someone in Hyderabad and the cultural differences make a deep-dive conversation with body language a lot harder to pull off. So I ask them to whip up a demo program that scores a game of Bowling, take as long as necessary, and bring the results to the interview and show me what they did. Not much but it works (and scoring a bowling game is actually not a bad test -- not as trivial as it sounds, but doesn't take a whole evening of work just for an interview).