Wood 250m official built by one of the best = $ 1 mi only the track - Plus cover, with 700 seated places and complete, I said complete infra it reached $ 4 mi at Rio de Janeiro Pan Games 2007.
Concrete - serious steady and reliable well shaped track is more expensive than $1 mi, if you want it to last, no cracks and moves etc. Can be from $ 2 to 3 mi, only the track, few infra around, no cover, of course.
Ok, you can just shape a piece of land and cover with 2" of "thin wire structured concrete" = it won't last, I believe. Many examples.
And about Detroit... great iniciative, but.. many many hopes, for a non-official footage track, without seats, etc.
https://www.crainsdetroit.com/sports...sustainability