Apples and oranges, but you know that.
If a private business wants to see my vaccine card, I have the choice whether to give them my business. I suspect if its a concert I really wanted to go to I would gladly show my vaccine card. In other cases, I'm probably taking my business elsewhere.
We will not require our customers to show a vaccine card, because its none of our f'ing business. This is decision that took less than a couple seconds to make.
There is this dangerous trend of the "infantilization" of adults (this is particularly distasteful when its done to minorities). IMO, requiring vaccine cards instead of using the honor system is an example of this.
Now who do you suppose would take unfair advantage of your "honor system"?