Racing was fun as hell when I was a teenager. Racers have been attaching their feet to the pedals for at least 88 years now (see the second and third photos):
https://www.welovecycling.com/wide/2...our-de-france/
They are not required to, and neither are any other cyclists. If you want to try racing, I would get used to clipless pedals, and then, get used to riding in a group, and in pace-lines with other riders. Just find a club ride with a regular meeting time and show up.
Luckily, racing and going fast are not needed to enjoy cycling!