I don’t know if not charging for memberships would cause a price increase (at least directly to make up for membership revenue)

I think instead it’s a more binding loyalty program. Most people will only get a membership to one warehouse club. So once they have someone locked in a membership, they are very unlikely to shop elsewhere. Customers will be more likely to shop exclusively at their store. And getting people in the door is half the battle for grocery stores. They can then hope to pump up tabs with enticing impulse buys and high margin items