Sourdough starter - Have I been doing it wrong?
You're fine. The reason to discard starter when you feed it is so that you don't end up with exponentially more starter and rapidly run out of room for it. You can slow down the growth of your starter and thus the need for frequent discards by keeping it in the refrigerator and feeding it once a week rather than every day. I've been doing this for about two years now. 

If you prefer, and if you have time, there are a number of things you can make with the "unfed" starter, rather than discarding it. I personally like the pancakes/waffles (same ingredients, different technique) from King Arthur Flour.