I think they have it, it's called free style. Everyone does the same stroke because it's the fastest even if that particular swimmer is best at back stroke or whatever.
ok, so I was mistaken in thinking that the stroke was called "freestyle" - the stroke that is used is more commonly known as the front crawl or australian crawl - so have one set of races with that stroke, and another set where any OTHER stroke is used (swimmer's choice)
How about Olympic events for ordinary folk? Swimming the dog paddle, walking a straight line, sitting on the horse, hanging from the bar, or maybe sitting at the bar? I think we could even figure out how to make Synchronized Rhythmic Horse Walking work for everyday people.