Management is about directing resources. Good management needs leadership ability to get the people they are directing to buy into where they are being directed, but also a bunch of other skills.
That being said, having the formal designation makes relationship and reputation building easier to start- subordinates are motivated to have a good relationship with you.
But if I don’t genuinely like and respect my manager, I’m not going to go the extra mile for him, I’m not going to stick it out with him through thick and thin and I’m going to leave at the first opportunity.
On the other hand, I’ve had very technical managers that their subordinates liked. But didn’t build positive relationships with the rest of the org. It was impossible to get things done that required cross team coordination and he couldn’t get the raises and recognition that his team wanted. Everyone ended up leaving.