The chain does not stretch, it just wears away.
That is the link pins (rivets) wear by abrasion.
All cycle chains use a hardened chrome steel rivet that will rust.
You have approx 100 of these, so if each wears 2/1000 inch that equals an extra 0.2" chainlength, or nearly half a 'link'.
It is recommended to change the chain before 1% extension, which is only 0.5" on the whole length, or just 5/1000" wear in each link.
Wear is faster on a derailleur geared bike because of the lateral bending that constantly moves grit through the link.
This is why a wax lube is the best, it keeps the muck out and is flexible.
So for the best life on a SS, I recommend the KMC Z610RB Rustbuster Singlespeed in 3/32" width at £6 delivered from CRC.
Go on, spoil yourself.