Thanks for the feedback! If you're familiar with vehicle cameras in games, there are camera-led systems and then basically everything else.
Because I envisioned a sweaty speedrun-type game, I always felt that camera-led wasn't the way to go. However, I did want to imitate that effect, for the reason that when you're turning left in a car, you look left so that you know what you're turning into, and then your look evens out as the turn completes.
Maybe you didn't notice, but the first person camera should have had the same look-ahead behavior as the third person camera...
If you're interested, there are a lot of camera settings you can tweak, and you can mess around with this look ahead behavior as well [see the tooltips].