There already are, they're called ultramarathons [0], 587 km would be on the longer end for a regularly held race but it's only slightly longer than Dean Karnazes's record for an uninterrupted run which was 560 km in 80 hours [1] so it'd be a multi day race probably.

[0] https://en.wikipedia.org/wiki/Ultramarathon

[1] https://en.wikipedia.org/wiki/Dean_Karnazes#Running_highligh...

Usually the extremely long distance ultra events are held as laps around a limited area because it's hard to safely run a race over hundreds of kilometers over a long period. Each racer needs a support car usually in the really long distance events that do happen to be run on roads etc. blocking traffic and making sure if they do get into medical trouble they can get help immediately.