Proprietary blend, open label, whatever. It's all just marketing.
If you had some product where you found that it works wonders if you just mix these 3 ingredients in a specific amount - and the ratio made a HUGE difference so that the proprietary product worked but any knockoff that didn't know that ratio would NOT work; then in theory a proprietary formula would make some sense.
But in reality, most supplements are way over hyped and they are only selling that possibility, not the actual reality. People think, "Oh, this is the ORIGINAL and they have a proprietary formula, that's why all the knock-offs don't give the same results". But the truth is, the original doesn't give results either.
Or they have a trademarked name for an easily sourced ingredient, etc.
And then on the flip side - some competitors can play the other card - "Look, we're open label". Nothing to hide here. And they spin that and some people will buy it based on that.
And why would a company do it both ways? Lots of situations, but I suspect "self selection" has a lot to do with it. Why does Kraft make their own Mac N Cheese but also make Mac N Cheese for the super market with the super market's brand on it (not saying they actually do - but companies do and this is a hypothetical example)? They do this because they know that some people will pay $2 for a box of Mac N Cheese and some will pay $1. How do you get the people who are willing to pay $2 to pay $2 while not losing any sales from people who are only willing to spend $1? You change the label and the customers will self select their price point. I suspect similar theory plays in here.