As a leader, being reliable and responsible is important for your team. You stand a good chance in gaining the trust of your team if you show that you exercise caution, take calculated risks, and will hold to the organizational principles.

Adjusting to a new leadership role can take some time. After a while, we will become more comfortable, and we may stop paying attention to our reputations.

Too much focus on data and analyses can detract from the broader context or the impact of your decisions. Relying only on data may indicate the best course of action for the bottom line, but it may not be the best decision for the team or relevant stakeholders.

There is a degree of responsibility (and professionalism) that is expected from those in charge.
Trying to be the fun boss will harm your reputation eventually. It is good to keep some space between you and your team.