I used to go shopping with a list.
However I found that I did not stick to the list and bought far more than was on the list -I am a compulsive buyer.
So, I changed by way of shopping some years ago when I was forced to after a bad accident -I shop online and get it delivered.
That way, I cannot buy impulsively which I can do if I go in to the shop with a list.
This is for me still far cheaper than physically going into a shop, so the answer to your question is definitely YES, as my list starts online early in the week and continues till I have enough to do an order.
When do do our main grocery shop, we have a list, but not when doing our secondary grocery shop or any other form of shopping. We always get stuff that is not on the list, but those are usually items that we always get, and don't need to write on the list to remember. We also take opportunities of special wine offers when they are on.
When I have my three little kids in tow I make sure to write a list before I go, that way I can remember what I wanted to buy despite being asked by three different people for all the lovely treats they want! It also helps keep spending in check as I can tell the kids that I'm only buying what's on the list sometimes (like when I'm low on funds). I do buy things not on the list sometimes because I get to the shop and realise I don't have this or that that I need too.
The only time I have a list is when I'm shopping for a particular recipe and don't have the ingredients in my pantry or fridge. I'm an impulsive buyer and as i have a large walk-in pantry, I buy on special. My children and grandchildren say I could feed half a 3rd world population.
Well, sort of! I've a thick, feint-ruled Notebook, & as I think of a required grocery item, or any other item, I write it down, or I'll forget about it, when I get to the shops!
Then I'll get home, & suddenly realise I forget to get the *insert forgotten item here*!
When I get to shops, I'll sit down, with a nice Mugachino, & peruse list! That way it refreshes my memory what's priority to be bought.
Conversely I also cross-off items no longer wanted!
So it's a bit 50/50 with me!