Sanjeev, Team leader it doesnt mean you should be a CEO or be a part of board room.
To lead your team, to tel your staff that you are with them, motivate them at work level, understand their problems,resolve it all these things comes under a team leader.
Gandhiji, Tilak never studied HR or not being a part of any board room or not a CEO. But they were great team leaded.A great potential to influence on people.Similarly now a days every dept staff having some dissatisfaction about their senior or reporting head such as production,marketing. In such a situation only HR who could understand them and act as a leader...I hope now its clear to you.
In case of people handling its a skill which differ from HR to HR . In my organization it is a very important skill for me. Might be not necessary for your org.