"every species becomes either space-faring, or extinct"
Which species are you using as examples in this statement?
You've been modded insightful but I think the modders don't understand the meaning of that word.
There are no examples of any species becoming "space-faring" while there are a lot of species here on earth that have been around for millions of years (us included) and which have no indications of going extinct any time soon (read for several more million years).
This planet will become uninhabitable eventually. Therefore, any species that does not develop spaceflight and leave the planet will die with it.