Writing from the country where the sourdough comes from, there are still bakers who make pure sourdough bread, for those who find yeast or wheat hard to digest. Sourdough bread is mainly a rye bread.
The sourdough bread takes 48 hours. You can only buy it at the bakers on Tuesdays.
When we went back to the UK for 5 years, I made bread with a dough starter for years and always mixed in a bit of yeast for a better effect. I started the bread and let it rise over night and like in Germany used part Rye flour.
When you are mixing / kneading before letting it rise you take a handful and put it in jamjar in the fridge. You then use that, the next time you bake. This is what the settlers in New America did, but then they baked everyday.
I found the fact that it was waiting for me to bake yet again, got on my nerves and when we had no family at home I gave it up. We have excellent bakers in Germany and they have had a 5 year apprenticeship!