If Managers were good with going with their gut and eyes - then nobody would have developed predictive models. The reality is Managers are often terrible at this and it can be very difficult to pull this off correctly.
Here's an example. DS is off to a hot start and the Jays consider whether he should become a starter. The predictive model still suggests the Varsho and KK give them the best chance to win, but they decide to override the model and start DS regardless of the matchup. DS goes 0-12 in 3 straight starts, but that's a really small sample size, so do you continue to override the model and start DS? or do you go back to Varsho/KK? Hot and cold streaks come and go without any indication or warning. Do you keep going with your gut over the non-bias, statistical data?
I fully expect the Jays predictive model suggests that starting DS in certainly matchups will yield the best results. And one could argue the model is working beautifully, as they are getting good production out of DS to date! You can suggest "most fans" don't agree with their predictive models - but what on earth is that based on? You don't even know what the models are based on or how accurate they've been. You're basing this on your eye test and the results? I mean my eye test showed me people were arguing Clement should start over IKF in the 2nd game vs. Seattle....yet IKF went 3-4. In fact, if left to the fans, Clement would have be starting over IKF almost every single day...yet here we are with IKF rocking a 131 wRC+ and Clement at 88. Fans were wrong all the time. Gut feelings are wrong all the time - hence why we use so much advanced statistics now.