It depends if they pass the savings on to the customer. if they're just finding more ways to gouge, then no. Aldis charges for bags, and I've set my trunk up with a carrier specifically for groceries from Aldis. Yes it's not as convenient. I have to push my shopping cart out to my car and load the items into the trunk carrier one by one, and since the shopping cart requires a refundable quarter, I have to push the cart back to the cart area. But a typical cart load at Aldis costs me almost half of a typical cart load from Walmart.
To be honest about what seems like big savings, I have to confess that I have to buy some things from other stores, because Aldis has a limited inventory, and most of those "other" things are higher priced items, although not actually necessary in my diet. But I still want them, so I also shop at Walmart. Otherwise, I would never step a foot into that place, anymore (at one time, I thought Walmart was the end all and be all of savings).
Now if you're dead set on on bags, you can still pay a nickle each for bags at Aldis. It may cost you another 30 cents for the trip, and you will still have to bag the stuff yourself, so if convenience is your deciding factor, you may want to shop someplace else. But the way I look at it is every time I walk out of Aldis, I'm $40 richer.