When companies try to become more data-driven, something that I find very often is the tendency to just follow the initial gut feeling process but this time find some supporting data without actually be open and objective.
But I also acknowledge the fact that data is what it is: A pile of information trying to gather via imperfect processes and imperfect representations.
I constantly get back to something I did hear around the topic of marketing attribution couple of years ago: "The new right is the less wrong".
Clearly you can make many mistakes gathering and analyzing data. But your domain knowledge should also help you identify clear mistakes and improve on them. Which then leads to a better data quality (hopefully you stayed objective enough to not create large biased data points).
But for me the most fundamental advantage remains:
Bringing data makes it easy to test and verify assumptions. You are bringing the full package to the table instead of a hard to qualify able / quantifiable feeling that often times is not easy to communicate.
The last element on this Data vs Human input: The limit quite often for algorithms to work perfectly is having all the information available. That is in many situations a real challenge, so the domain knowledge helps to fill in gaps.