Just trust me, it's disgusting. I expect it's because all the lactase that the lacto bacteria are generating is useless, since the lactose has already been broken down when the milk is made. So I think that lets other bacteria thrive, and I dunno, maybe the lacto bacteria like glucose, which has been filtered out of the milk, and so the galactose is all there is.
It's disgusting, so just don't try it, because I did and it was terrible.
It wasn't as gross as the time my kid and I tried using ant-hill dirt as a yogurt starter. I threw away the jar after I took the lid off for a millisecond to smell it and holy smokes, folks. Maybe I had a bad ant hill.
And before my zero readers ask themselves why I'd do that, it's because I read somewhere that the bacteria live in ant hills. This makes sense, as people apparently used to milk cows in buckets and just carried the open bucket around everywhere. So some people invariably died of horrible diseases from junk that got into the milk, but also some ant dirt must have dropped into some and turned into delicious yogurt, so there is that.