why did the professional sport draft begin?

Answer 1

To make teams more competitive since the teams with more money could go out and outbid for any player. Before Curt Flood in the 70's there were no true free agents. Yes you could be signed by another team but it acted as a trade or sale since the team you came from would get something in return

Answer 2

Which sport are you referring to? The first NBA Draft was
held in 1947. The NFL Draft has been held since 1936.
The NHL Entry Draft has been in existence until 1963.
The MLB Draft has been in existence since 1965. I guess
the answer is 1936 if we base it on the oldest draft pick.