The problem with using gut feeling and hiring somebody that "belongs in your team" is that you fail to find diversity.
I am not going to argue about quotas, and trying to hire diverse people just to force diversity into the team or company, that is not the way to go.
But diversity in a team is a very valuable asset. Having people with distinct points of view, different ways to approach problems, or just the capacity to see the world in a different way are all key to get a better product.
And you are not going to get that when you interview thinking on "fits the culture of the company" of "belongs in our team", because you are just hiring more and more people that thinks and behaves the same way.
The way to get diversity is to try to identify your bias and work around it (everybody has unconscious bias, even after training, you cannot remove, but you can know you have it and prevent it to guide your decisions).
Trying to get a subjective process is not that difficult, you just need to focus on the objective qualities of the candidate, not on the feeling. That's the main reason why you take notes during your interview, it is to read them after the interview, and focus on the subjective markers, not on how you feel during the interview.
I wrote a little about it (https://medium.com/@dmunozg/wrapping-the-code-interview-d400bca4dc4b?source=friends_link&sk=ccd9ff78b94541dfbb5c3603d6b516fa) if you want to read more.