(I'm guessing that there was more money in professional sport in the US in the 70's so you may have to go back a few years there to see a similar situation)
The situation started changing in the US in the 1970s because the players in the largest pro sports, major league baseball and pro football started to organize.
In baseball especially, there was a mechanism called the
reserve clause, which bounded a player to a certain team for life. The team and the team owner had all the control over salaries, players movement, etc. The player had no recourse over their contract and salaries were kept artificially low because the owner had that lifetime binding.
A series of court decisions between 1969-1974 the changed this. At the beginning was 2-year case of baseball outfielder Curt Flood, who essentially sued to challenge reserve clause because his team traded him to another team and he refused to report to the team he was traded to.
Flood lost 2 years of his career fighting the clause, but his fight led to a decision in 1974 in a case involving MLB player Dave McNally and Andy Messersmith, who both sued for the right to decide who their employers would be after their contracts with the current team expired. That brought free agency to pro sports, and the salaries accelerated now that players had a great right of free movement.
But the situation we see today did not came to pass truly in the mid 1980s, when you had a situation where both Major League Baseball and the National Football League each suffered two work stoppages in the decade. The results of both eventually further opened up free agency and gave the players a greater margin of collective control of their labor.
Now different sports have seen a different evolution. Consider how motor racing changed, and that too didn't see what we have now into the 1980s. And in many ways the changes impired by drivers and team owner have made the sport more lucrative and safer, but on the downside the sport has a stratification and specialization today which, in my opinion, has taken away some of the magic and global scope of the sport. In the 1960s and 1970s it wasn't uncommon to see a Grand Prix star also show up in Indiana in the month of May. It wasn't uncommon to see teams of American dirt track aces and Indy superstars go two around the clock at LeMans. Today, unless you have a heavy lorry full of Pounds, you will not see Lewis Hamilton in the Indy 500, or a team consisting of Ryan-Hunter Reay, Marco Andretti and Kyle Busch taking on Tom Kristensen and Dindo Capello at LeMans.