I am very confident this is the case. When we have a well-oiled culture of reuse it will be easy and cheap to just show up with your various containers and do your shopping.
Labor is the biggest expense for businesses, and anything that increases number of man hours means higher costs.
Plastic wrapped items make it very easy for customers to shop themselves with minimal interaction from staff and for the store to still guarantee cleanliness standards. I can only imagine that people coming in with their own containers will require more staff to follow proper protocols in dispensing items and whatnot, resulting in higher costs.
Maybe even take it a step further and have standardized containers that you can drop off when you go shopping in exchange for clean ones and use those. The ones you dropped off can be sent off to a facility to deep clean them, similar to how beer bottles work.
A grocery store I used to live near had a hookup like this with a local dairy farm for their glass bottle milk. iirc returning the bottle also got you like $.25 off the next gallon at checkout.
