There used to be matches for 3rd place in a lot of events-but the practice died out because no one took them seriously-least of all the players themselves.
Pam Shriver had a 3rd place match with Steffi Graf at the Slims Chmps (=the WTA finals) one year. I can't recall the details. It was more or less decided who was going to win their 3rd place-or maybe Pammy or Steffi tanked it.
The whole idea was to get off the court ASAP.
With the Olympics it's different because you're playing for a bronze medal-and it might be your only shot a medal your whole life.
In tennis there's always another day-and who cares about 3rd?