I would stick with the original rules. The actual effect your house rule has on game balance is probably negligible. Most of the time you won't end up drawing anyone's discard anyway, and even when you do it's only slightly better on average than a random card (unless you were the one who discarded it, in which case it's a lot worse). Thus even if balance is fractionally improved (and I'm not convinced it is), I'd focus instead on a few other effects:
- Shuffling a lot is annoying and makes the game take longer. (thanks @Othya for pointing this out in the comments)
- For me at least, drawing my own discard would feel like the game giving me the middle finger - sure there are other useless cards I could have drawn, but I'd feel particularly screwed over by getting the same worthless card twice.
As a side note, I don't quite use the original rules myself - I make a separate discard pile and then shuffle it when the deck runs out.