Certainly it would be strange, but I am not sure that making the ‘racing’ aspect optional would be truly absurd. The competitor who crosses 100m in the shortest time would still win, it would just be a choice as to whether they ran a race, ran catch up, or ran on there own. Tactically it would ad an element or two. There would have to be a duration over which the race could take place (maybe 5 minutes) and any valid run would have to occur within that period.
Still this is only a thought game. I would still like to know if anyone has measured the time difference between competitors in leaving the blocks (not how good a start they get, but how quickly their rear foot leaves the block) in an Olympic sprint. And is this time difference of similar magnitude to the differnece between coming first and second (or first and forth).