Does couponing actually make things cheaper than shopping store brands or at Aldi?

I'm a self-proclaimed cynic, to a fault. I drive my wife crazy with how negative and distrusting I can be with almost any company.

That being said, my understanding of most coupons or store sales is that Store A sells peanut butter for $2. Store B sells peanut butter for $3, but puts out a coupon for 20% off for a total of $2.40. People see the 20% discount and buy that store's peanut butter, assuming it's a good deal.

Store's like Joanne drive me crazy for this reason. Their big thing is saying that there are so many coupons that you can't help but get great deals! Meanwhile if you buy anything for regular price it's a big markup compared to Amazon or other stores.

Again, I apologize for being so negative and cynical, but in your opinion is this the reality of couponing? Or does it actually save money over buyng from a store that never offers deals or coupons and just has low prices in general?

Thanks!